--- a/Notes.md	Fri Mar 18 20:44:17 2022 +0100
+++ b/Notes.md	Fri Mar 18 21:14:47 2022 +0100
@@ -132,10 +132,10 @@
  * When doing specialised computations for different parts of the range/domain?
  * More?
 
- Maybe if we should have dynamic sizing it could be only for the range. `domain_size` would not be implemented. And the `range_size` would be a function of a vector that the TensorMapping is applied to.
+ Maybe if we should have dynamic sizing it could be only for the range. `domain_size` would not be implemented. And the `range_size` would be a function of a vector that the LazyTensor is applied to.
 
 ## Reasearch and thinking
- - [ ] Use a trait to indicate that a TensorMapping har the same range and domain?
+ - [ ] Use a trait to indicate that a LazyTensor har the same range and domain?
  - [ ] Rename all the Tensor stuff to just LazyOperator, LazyApplication and so on?
  - [ ] Check how the native julia doc generator works
     - [ ] Check if Vidars design docs fit in there
@@ -145,15 +145,15 @@
  - [ ] Dispatch on Lower() instead of the type Lower so `::Lower` instead of `::Type{Lower}` ???
  	Seems better unless there is some specific reason to use the type instead of the value.
  - [ ] How do we handle mixes of periodic and non-periodic grids? Seems it should be supported on the grid level and on the 1d operator level. Between there it should be transparent.
- - [ ] Can we have a trait to tell if a TensorMapping is transposable?
+ - [ ] Can we have a trait to tell if a LazyTensor is transposable?
  - [ ] Is it ok to have "Constructors" for abstract types which create subtypes? For example a Grids() functions that gives different kind of grids based on input?
  - [ ] Figure out how to treat the borrowing parameters of operators. Include in into the struct? Expose via function dispatched on the operator type and grid?
 
 ## Regions and tensormappings
-- [ ] Use a trait to indicate if a TensorMapping uses indices with regions.
+- [ ] Use a trait to indicate if a LazyTensor uses indices with regions.
     The default should be that they do NOT.
         - [ ] What to name this trait? Can we call it IndexStyle but not export it to avoid conflicts with Base.IndexStyle?
- - [ ] Figure out repeated application of regioned TensorMappings. Maybe an instance of a tensor mapping needs to know the exact size of the range and domain for this to work?
+ - [ ] Figure out repeated application of regioned LazyTensors. Maybe an instance of a tensor mapping needs to know the exact size of the range and domain for this to work?
 
 ## Boundschecking and dimension checking
 Does it make sense to have boundschecking only in getindex methods?
@@ -261,16 +261,16 @@
 Vi kan ha tensor-operatorer som agerar på ett skalärt fält och ger ett vektorfält eller tensorfält.
 Vi kan också ha tensor-operatorer som agerar på ett vektorfält eller tensorfält och ger ett skalärt fält.
 
-TBD: Just nu gör `apply_transpose` antagandet att domän-typen är samma som range-typen. Det behöver vi på något sätt bryta. Ett alternativ är låta en TensorMapping ha `T_domain` och `T_range` istället för bara `T`. Känns dock lite grötigt. Ett annat alternativ skulle vara någon typ av trait för transpose? Den skulle kunna innehålla typen som transponatet agerar på? Vet inte om det fungerar dock.
+TBD: Just nu gör `apply_transpose` antagandet att domän-typen är samma som range-typen. Det behöver vi på något sätt bryta. Ett alternativ är låta en LazyTensor ha `T_domain` och `T_range` istället för bara `T`. Känns dock lite grötigt. Ett annat alternativ skulle vara någon typ av trait för transpose? Den skulle kunna innehålla typen som transponatet agerar på? Vet inte om det fungerar dock.
 
-TBD: Vad är målet med `T`-parametern för en TensorMapping? Om vi vill kunna applicera en difference operator på vad som helst kan man inte anta att en `TensorMapping{T}` bara agerar på instanser av `T`.
+TBD: Vad är målet med `T`-parametern för en LazyTensor? Om vi vill kunna applicera en difference operator på vad som helst kan man inte anta att en `LazyTensor{T}` bara agerar på instanser av `T`.
 
 Man kan implementera `∇` som en tensormapping som agerar på T och returnerar `StaticVector{N,T} where N`.
 (Man skulle eventuellt också kunna låta den agera på `StaticMatrix{N,T,D} where N` och returnera `StaticMatrix{M,T,D+1}`. Frågan är om man vinner något på det...)
 
-Skulle kunna ha en funktion `range_type(::TensorMapping, ::Type{domain_type})`
+Skulle kunna ha en funktion `range_type(::LazyTensor, ::Type{domain_type})`
 
-Kanske kan man implementera `⋅(tm::TensorMapping{R,D}, v::AbstractArray{T,D})` där T är en AbstractArray, tm på något sätt har komponenter, lika många som T har element.
+Kanske kan man implementera `⋅(tm::LazyTensor{R,D}, v::AbstractArray{T,D})` där T är en AbstractArray, tm på något sätt har komponenter, lika många som T har element.
 
 ### Ratade alternativ:
 
@@ -302,7 +302,7 @@
 En viktig operation för vektor fält är att kunna få ut komponenter som grid-funktioner. Detta behöver antagligen kunna ske lazy.
 Det finns ett par olika lösningar:
 * Implementera en egen typ av view som tar hand om detta. Eller Accessors.jl?
-* Använda en TensorMapping
+* Använda en LazyTensor
 * Någon typ av lazy-broadcast
 * En lazy array som applicerar en funktion för varje element.
 
@@ -349,4 +349,4 @@
 
 
 ## Name of the `VolumeOperator` type for constant stencils
-It seems that the name is too general. The name of the method `volume_operator` makes sense. It should return different types of `TensorMapping` specialized for the grid. A suggetion for a better name is `ConstantStencilVolumeOperator`
+It seems that the name is too general. The name of the method `volume_operator` makes sense. It should return different types of `LazyTensor` specialized for the grid. A suggetion for a better name is `ConstantStencilVolumeOperator`

--- a/TODO.md	Fri Mar 18 20:44:17 2022 +0100
+++ b/TODO.md	Fri Mar 18 21:14:47 2022 +0100
@@ -12,7 +12,7 @@
  - [ ] Make sure we are setting tolerances in tests in a consistent way
  - [ ] Add check for correct domain sizes to lazy tensor operations using SizeMismatch
  - [ ] Write down some coding guideline or checklist for code conventions. For example i,j,... for indices and I for multi-index
- - [ ] Add boundschecking in TensorMappingApplication
+ - [ ] Add boundschecking in LazyTensorApplication
  - [ ] Start renaming things in LazyTensors
  - [ ] Clean up RegionIndices
     1. [ ] Write tests for how things should work

--- a/src/LazyTensors/LazyTensors.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/LazyTensors/LazyTensors.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,12 +1,12 @@
 module LazyTensors
 
-export LazyTensorMappingApplication
-export LazyTensorMappingTranspose
-export TensorMappingComposition
+export LazyTensorApplication
+export LazyTensorTranspose
+export LazyTensorComposition
 export LazyLinearMap
-export IdentityMapping
+export IdentityTensor
 export ScalingTensor
-export InflatedTensorMapping
+export InflatedLazyTensor
 export LazyOuterProduct
 export ⊗
 export SizeMismatch

--- a/src/LazyTensors/lazy_tensor_operations.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/LazyTensors/lazy_tensor_operations.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,19 +1,19 @@
 # TBD: Is there a good way to split this file?
 
 """
-    LazyTensorMappingApplication{T,R,D} <: LazyArray{T,R}
+    LazyTensorApplication{T,R,D} <: LazyArray{T,R}
 
-Struct for lazy application of a TensorMapping. Created using `*`.
+Struct for lazy application of a LazyTensor. Created using `*`.
 
-Allows the result of a `TensorMapping` applied to a vector to be treated as an `AbstractArray`.
-With a mapping `m` and a vector `v` the LazyTensorMappingApplication object can be created by `m*v`.
+Allows the result of a `LazyTensor` applied to a vector to be treated as an `AbstractArray`.
+With a mapping `m` and a vector `v` the LazyTensorApplication object can be created by `m*v`.
 The actual result will be calcualted when indexing into `m*v`.
 """
-struct LazyTensorMappingApplication{T,R,D, TM<:TensorMapping{<:Any,R,D}, AA<:AbstractArray{<:Any,D}} <: LazyArray{T,R}
+struct LazyTensorApplication{T,R,D, TM<:LazyTensor{<:Any,R,D}, AA<:AbstractArray{<:Any,D}} <: LazyArray{T,R}
     t::TM
     o::AA
 
-    function LazyTensorMappingApplication(t::TensorMapping{<:Any,R,D}, o::AbstractArray{<:Any,D}) where {R,D}
+    function LazyTensorApplication(t::LazyTensor{<:Any,R,D}, o::AbstractArray{<:Any,D}) where {R,D}
         I = ntuple(i->1, range_dim(t))
         T = typeof(apply(t,o,I...))
         return new{T,R,D,typeof(t), typeof(o)}(t,o)
@@ -21,103 +21,103 @@
 end
 # TODO: Do boundschecking on creation!
 
-Base.getindex(ta::LazyTensorMappingApplication{T,R}, I::Vararg{Any,R}) where {T,R} = apply(ta.t, ta.o, I...)
-Base.getindex(ta::LazyTensorMappingApplication{T,1}, I::CartesianIndex{1}) where {T} = apply(ta.t, ta.o, I.I...) # Would otherwise be caught in the previous method.
-Base.size(ta::LazyTensorMappingApplication) = range_size(ta.t)
+Base.getindex(ta::LazyTensorApplication{T,R}, I::Vararg{Any,R}) where {T,R} = apply(ta.t, ta.o, I...)
+Base.getindex(ta::LazyTensorApplication{T,1}, I::CartesianIndex{1}) where {T} = apply(ta.t, ta.o, I.I...) # Would otherwise be caught in the previous method.
+Base.size(ta::LazyTensorApplication) = range_size(ta.t)
 # TODO: What else is needed to implement the AbstractArray interface?
 
-Base.:*(a::TensorMapping, v::AbstractArray) = LazyTensorMappingApplication(a,v)
-Base.:*(a::TensorMapping, b::TensorMapping) = throw(MethodError(Base.:*,(a,b)))
-Base.:*(a::TensorMapping, args::Union{TensorMapping, AbstractArray}...) = foldr(*,(a,args...))
+Base.:*(a::LazyTensor, v::AbstractArray) = LazyTensorApplication(a,v)
+Base.:*(a::LazyTensor, b::LazyTensor) = throw(MethodError(Base.:*,(a,b)))
+Base.:*(a::LazyTensor, args::Union{LazyTensor, AbstractArray}...) = foldr(*,(a,args...))
 
 # # We need the associativity to be a→b→c = a→(b→c), which is the case for '→'
 # # Should we overload some other infix binary opesrator?
-# →(tm::TensorMapping{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorMappingApplication(tm,o)
+# →(tm::LazyTensor{T,R,D}, o::AbstractArray{T,D}) where {T,R,D} = LazyTensorApplication(tm,o)
 # TODO: We need to be really careful about good error messages.
-# For example what happens if you try to multiply LazyTensorMappingApplication with a TensorMapping(wrong order)?
+# For example what happens if you try to multiply LazyTensorApplication with a LazyTensor(wrong order)?
 
 """
-    LazyTensorMappingTranspose{T,R,D} <: TensorMapping{T,D,R}
+    LazyTensorTranspose{T,R,D} <: LazyTensor{T,D,R}
 
-Struct for lazy transpose of a TensorMapping.
+Struct for lazy transpose of a LazyTensor.
 
 If a mapping implements the the `apply_transpose` method this allows working with
-the transpose of mapping `m` by using `m'`. `m'` will work as a regular TensorMapping lazily calling
+the transpose of mapping `m` by using `m'`. `m'` will work as a regular LazyTensor lazily calling
 the appropriate methods of `m`.
 """
-struct LazyTensorMappingTranspose{T,R,D, TM<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
+struct LazyTensorTranspose{T,R,D, TM<:LazyTensor{T,R,D}} <: LazyTensor{T,D,R}
     tm::TM
 end
 
 # # TBD: Should this be implemented on a type by type basis or through a trait to provide earlier errors?
-# Jonatan 2020-09-25: Is the problem that you can take the transpose of any TensorMapping even if it doesn't implement `apply_transpose`?
-Base.adjoint(tm::TensorMapping) = LazyTensorMappingTranspose(tm)
-Base.adjoint(tmt::LazyTensorMappingTranspose) = tmt.tm
+# Jonatan 2020-09-25: Is the problem that you can take the transpose of any LazyTensor even if it doesn't implement `apply_transpose`?
+Base.adjoint(tm::LazyTensor) = LazyTensorTranspose(tm)
+Base.adjoint(tmt::LazyTensorTranspose) = tmt.tm
 
-apply(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D} = apply_transpose(tmt.tm, v, I...)
-apply_transpose(tmt::LazyTensorMappingTranspose{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
+apply(tmt::LazyTensorTranspose{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D} = apply_transpose(tmt.tm, v, I...)
+apply_transpose(tmt::LazyTensorTranspose{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmt.tm, v, I...)
 
-range_size(tmt::LazyTensorMappingTranspose) = domain_size(tmt.tm)
-domain_size(tmt::LazyTensorMappingTranspose) = range_size(tmt.tm)
+range_size(tmt::LazyTensorTranspose) = domain_size(tmt.tm)
+domain_size(tmt::LazyTensorTranspose) = range_size(tmt.tm)
 
 
-struct LazyTensorMappingBinaryOperation{Op,T,R,D,T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}} <: TensorMapping{T,D,R}
+struct LazyLazyTensorBinaryOperation{Op,T,R,D,T1<:LazyTensor{T,R,D},T2<:LazyTensor{T,R,D}} <: LazyTensor{T,D,R}
     tm1::T1
     tm2::T2
 
-    @inline function LazyTensorMappingBinaryOperation{Op,T,R,D}(tm1::T1,tm2::T2) where {Op,T,R,D, T1<:TensorMapping{T,R,D},T2<:TensorMapping{T,R,D}}
+    @inline function LazyLazyTensorBinaryOperation{Op,T,R,D}(tm1::T1,tm2::T2) where {Op,T,R,D, T1<:LazyTensor{T,R,D},T2<:LazyTensor{T,R,D}}
         return new{Op,T,R,D,T1,T2}(tm1,tm2)
     end
 end
 # TODO: Boundschecking in constructor.
 
-apply(tmBinOp::LazyTensorMappingBinaryOperation{:+,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) + apply(tmBinOp.tm2, v, I...)
-apply(tmBinOp::LazyTensorMappingBinaryOperation{:-,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) - apply(tmBinOp.tm2, v, I...)
+apply(tmBinOp::LazyLazyTensorBinaryOperation{:+,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) + apply(tmBinOp.tm2, v, I...)
+apply(tmBinOp::LazyLazyTensorBinaryOperation{:-,T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D} = apply(tmBinOp.tm1, v, I...) - apply(tmBinOp.tm2, v, I...)
 
-range_size(tmBinOp::LazyTensorMappingBinaryOperation) = range_size(tmBinOp.tm1)
-domain_size(tmBinOp::LazyTensorMappingBinaryOperation) = domain_size(tmBinOp.tm1)
+range_size(tmBinOp::LazyLazyTensorBinaryOperation) = range_size(tmBinOp.tm1)
+domain_size(tmBinOp::LazyLazyTensorBinaryOperation) = domain_size(tmBinOp.tm1)
 
-Base.:+(tm1::TensorMapping{T,R,D}, tm2::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:+,T,R,D}(tm1,tm2)
-Base.:-(tm1::TensorMapping{T,R,D}, tm2::TensorMapping{T,R,D}) where {T,R,D} = LazyTensorMappingBinaryOperation{:-,T,R,D}(tm1,tm2)
+Base.:+(tm1::LazyTensor{T,R,D}, tm2::LazyTensor{T,R,D}) where {T,R,D} = LazyLazyTensorBinaryOperation{:+,T,R,D}(tm1,tm2)
+Base.:-(tm1::LazyTensor{T,R,D}, tm2::LazyTensor{T,R,D}) where {T,R,D} = LazyLazyTensorBinaryOperation{:-,T,R,D}(tm1,tm2)
 
 """
-    TensorMappingComposition{T,R,K,D}
+    LazyTensorComposition{T,R,K,D}
 
-Lazily compose two `TensorMapping`s, so that they can be handled as a single `TensorMapping`.
+Lazily compose two `LazyTensor`s, so that they can be handled as a single `LazyTensor`.
 """
-struct TensorMappingComposition{T,R,K,D, TM1<:TensorMapping{T,R,K}, TM2<:TensorMapping{T,K,D}} <: TensorMapping{T,R,D}
+struct LazyTensorComposition{T,R,K,D, TM1<:LazyTensor{T,R,K}, TM2<:LazyTensor{T,K,D}} <: LazyTensor{T,R,D}
     t1::TM1
     t2::TM2
 
-    @inline function TensorMappingComposition(t1::TensorMapping{T,R,K}, t2::TensorMapping{T,K,D}) where {T,R,K,D}
+    @inline function LazyTensorComposition(t1::LazyTensor{T,R,K}, t2::LazyTensor{T,K,D}) where {T,R,K,D}
         @boundscheck check_domain_size(t1, range_size(t2))
         return new{T,R,K,D, typeof(t1), typeof(t2)}(t1,t2)
     end
 end
 
-range_size(tm::TensorMappingComposition) = range_size(tm.t1)
-domain_size(tm::TensorMappingComposition) = domain_size(tm.t2)
+range_size(tm::LazyTensorComposition) = range_size(tm.t1)
+domain_size(tm::LazyTensorComposition) = domain_size(tm.t2)
 
-function apply(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,K,D}
+function apply(c::LazyTensorComposition{T,R,K,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,K,D}
     apply(c.t1, c.t2*v, I...)
 end
 
-function apply_transpose(c::TensorMappingComposition{T,R,K,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,K,D}
+function apply_transpose(c::LazyTensorComposition{T,R,K,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,K,D}
     apply_transpose(c.t2, c.t1'*v, I...)
 end
 
-Base.@propagate_inbounds Base.:∘(s::TensorMapping, t::TensorMapping) = TensorMappingComposition(s,t)
+Base.@propagate_inbounds Base.:∘(s::LazyTensor, t::LazyTensor) = LazyTensorComposition(s,t)
 
 """
     LazyLinearMap{T,R,D,...}(A, range_indicies, domain_indicies)
 
-TensorMapping defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should
-be considerd the range and domain of the TensorMapping. Each set of indices must be ordered in ascending order.
+LazyTensor defined by the AbstractArray A. `range_indicies` and `domain_indicies` define which indicies of A should
+be considerd the range and domain of the LazyTensor. Each set of indices must be ordered in ascending order.
 
 For instance, if A is a m x n matrix, and range_size = (1,), domain_size = (2,), then the LazyLinearMap performs the
 standard matrix-vector product on vectors of size n.
 """
-struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: TensorMapping{T,R,D}
+struct LazyLinearMap{T,R,D, RD, AA<:AbstractArray{T,RD}} <: LazyTensor{T,R,D}
     A::AA
     range_indicies::NTuple{R,Int}
     domain_indicies::NTuple{D,Int}
@@ -149,54 +149,54 @@
 
 
 """
-    IdentityMapping{T,D} <: TensorMapping{T,D,D}
+    IdentityTensor{T,D} <: LazyTensor{T,D,D}
 
-The lazy identity TensorMapping for a given size. Usefull for building up higher dimensional tensor mappings from lower
-dimensional ones through outer products. Also used in the Implementation for InflatedTensorMapping.
+The lazy identity LazyTensor for a given size. Usefull for building up higher dimensional tensor mappings from lower
+dimensional ones through outer products. Also used in the Implementation for InflatedLazyTensor.
 """
-struct IdentityMapping{T,D} <: TensorMapping{T,D,D}
+struct IdentityTensor{T,D} <: LazyTensor{T,D,D}
     size::NTuple{D,Int}
 end
 
-IdentityMapping{T}(size::NTuple{D,Int}) where {T,D} = IdentityMapping{T,D}(size)
-IdentityMapping{T}(size::Vararg{Int,D}) where {T,D} = IdentityMapping{T,D}(size)
-IdentityMapping(size::Vararg{Int,D}) where D = IdentityMapping{Float64,D}(size)
+IdentityTensor{T}(size::NTuple{D,Int}) where {T,D} = IdentityTensor{T,D}(size)
+IdentityTensor{T}(size::Vararg{Int,D}) where {T,D} = IdentityTensor{T,D}(size)
+IdentityTensor(size::Vararg{Int,D}) where D = IdentityTensor{Float64,D}(size)
 
-range_size(tmi::IdentityMapping) = tmi.size
-domain_size(tmi::IdentityMapping) = tmi.size
+range_size(tmi::IdentityTensor) = tmi.size
+domain_size(tmi::IdentityTensor) = tmi.size
 
-apply(tmi::IdentityMapping{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
-apply_transpose(tmi::IdentityMapping{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
+apply(tmi::IdentityTensor{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
+apply_transpose(tmi::IdentityTensor{T,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,D}) where {T,D} = v[I...]
 
 """
     Base.:∘(tm, tmi)
     Base.:∘(tmi, tm)
 
-Composes a `Tensormapping` `tm` with an `IdentityMapping` `tmi`, by returning `tm`
+Composes a `Tensormapping` `tm` with an `IdentityTensor` `tmi`, by returning `tm`
 """
-@inline function Base.:∘(tm::TensorMapping{T,R,D}, tmi::IdentityMapping{T,D}) where {T,R,D}
+@inline function Base.:∘(tm::LazyTensor{T,R,D}, tmi::IdentityTensor{T,D}) where {T,R,D}
     @boundscheck check_domain_size(tm, range_size(tmi))
     return tm
 end
 
-@inline function Base.:∘(tmi::IdentityMapping{T,R}, tm::TensorMapping{T,R,D}) where {T,R,D}
+@inline function Base.:∘(tmi::IdentityTensor{T,R}, tm::LazyTensor{T,R,D}) where {T,R,D}
     @boundscheck check_domain_size(tmi, range_size(tm))
     return tm
 end
-# Specialization for the case where tm is an IdentityMapping. Required to resolve ambiguity.
-@inline function Base.:∘(tm::IdentityMapping{T,D}, tmi::IdentityMapping{T,D}) where {T,D}
+# Specialization for the case where tm is an IdentityTensor. Required to resolve ambiguity.
+@inline function Base.:∘(tm::IdentityTensor{T,D}, tmi::IdentityTensor{T,D}) where {T,D}
     @boundscheck check_domain_size(tm, range_size(tmi))
     return tmi
 end
-# TODO: Implement the above as TensorMappingComposition instead
+# TODO: Implement the above as LazyTensorComposition instead
 # TODO: Move the operator definitions to one place
 
 """
-    ScalingTensor{T,D} <: TensorMapping{T,D,D}
+    ScalingTensor{T,D} <: LazyTensor{T,D,D}
 
 A lazy tensor that scales its input with `λ`.
 """
-struct ScalingTensor{T,D} <: TensorMapping{T,D,D}
+struct ScalingTensor{T,D} <: LazyTensor{T,D,D}
     λ::T
     size::NTuple{D,Int}
 end
@@ -211,16 +211,16 @@
 # TODO: Remove ScalingOperator from tests
 
 """
-    InflatedTensorMapping{T,R,D} <: TensorMapping{T,R,D}
+    InflatedLazyTensor{T,R,D} <: LazyTensor{T,R,D}
 
-An inflated `TensorMapping` with dimensions added before and afer its actual dimensions.
+An inflated `LazyTensor` with dimensions added before and afer its actual dimensions.
 """
-struct InflatedTensorMapping{T,R,D,D_before,R_middle,D_middle,D_after, TM<:TensorMapping{T,R_middle,D_middle}} <: TensorMapping{T,R,D}
-    before::IdentityMapping{T,D_before}
+struct InflatedLazyTensor{T,R,D,D_before,R_middle,D_middle,D_after, TM<:LazyTensor{T,R_middle,D_middle}} <: LazyTensor{T,R,D}
+    before::IdentityTensor{T,D_before}
     tm::TM
-    after::IdentityMapping{T,D_after}
+    after::IdentityTensor{T,D_after}
 
-    function InflatedTensorMapping(before, tm::TensorMapping{T}, after) where T
+    function InflatedLazyTensor(before, tm::LazyTensor{T}, after) where T
         R_before = range_dim(before)
         R_middle = range_dim(tm)
         R_after = range_dim(after)
@@ -234,35 +234,35 @@
     end
 end
 """
-    InflatedTensorMapping(before, tm, after)
-    InflatedTensorMapping(before,tm)
-    InflatedTensorMapping(tm,after)
+    InflatedLazyTensor(before, tm, after)
+    InflatedLazyTensor(before,tm)
+    InflatedLazyTensor(tm,after)
 
-The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityMapping`s.
+The outer product of `before`, `tm` and `after`, where `before` and `after` are `IdentityTensor`s.
 
-If one of `before` or `after` is left out, a 0-dimensional `IdentityMapping` is used as the default value.
+If one of `before` or `after` is left out, a 0-dimensional `IdentityTensor` is used as the default value.
 
-If `tm` already is an `InflatedTensorMapping`, `before` and `after` will be extended instead of
-creating a nested `InflatedTensorMapping`.
+If `tm` already is an `InflatedLazyTensor`, `before` and `after` will be extended instead of
+creating a nested `InflatedLazyTensor`.
 """
-InflatedTensorMapping(::IdentityMapping, ::TensorMapping, ::IdentityMapping)
+InflatedLazyTensor(::IdentityTensor, ::LazyTensor, ::IdentityTensor)
 
-function InflatedTensorMapping(before, itm::InflatedTensorMapping, after)
-    return InflatedTensorMapping(
-        IdentityMapping(before.size...,  itm.before.size...),
+function InflatedLazyTensor(before, itm::InflatedLazyTensor, after)
+    return InflatedLazyTensor(
+        IdentityTensor(before.size...,  itm.before.size...),
         itm.tm,
-        IdentityMapping(itm.after.size..., after.size...),
+        IdentityTensor(itm.after.size..., after.size...),
     )
 end
 
-InflatedTensorMapping(before::IdentityMapping, tm::TensorMapping{T}) where T = InflatedTensorMapping(before,tm,IdentityMapping{T}())
-InflatedTensorMapping(tm::TensorMapping{T}, after::IdentityMapping) where T = InflatedTensorMapping(IdentityMapping{T}(),tm,after)
+InflatedLazyTensor(before::IdentityTensor, tm::LazyTensor{T}) where T = InflatedLazyTensor(before,tm,IdentityTensor{T}())
+InflatedLazyTensor(tm::LazyTensor{T}, after::IdentityTensor) where T = InflatedLazyTensor(IdentityTensor{T}(),tm,after)
 # Resolve ambiguity between the two previous methods
-InflatedTensorMapping(I1::IdentityMapping{T}, I2::IdentityMapping{T}) where T = InflatedTensorMapping(I1,I2,IdentityMapping{T}())
+InflatedLazyTensor(I1::IdentityTensor{T}, I2::IdentityTensor{T}) where T = InflatedLazyTensor(I1,I2,IdentityTensor{T}())
 
-# TODO: Implement some pretty printing in terms of ⊗. E.g InflatedTensorMapping(I(3),B,I(2)) -> I(3)⊗B⊗I(2)
+# TODO: Implement some pretty printing in terms of ⊗. E.g InflatedLazyTensor(I(3),B,I(2)) -> I(3)⊗B⊗I(2)
 
-function range_size(itm::InflatedTensorMapping)
+function range_size(itm::InflatedLazyTensor)
     return flatten_tuple(
         range_size(itm.before),
         range_size(itm.tm),
@@ -270,7 +270,7 @@
     )
 end
 
-function domain_size(itm::InflatedTensorMapping)
+function domain_size(itm::InflatedLazyTensor)
     return flatten_tuple(
         domain_size(itm.before),
         domain_size(itm.tm),
@@ -278,7 +278,7 @@
     )
 end
 
-function apply(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
+function apply(itm::InflatedLazyTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg{Any,R}) where {T,R,D}
     dim_before = range_dim(itm.before)
     dim_domain = domain_dim(itm.tm)
     dim_range = range_dim(itm.tm)
@@ -290,7 +290,7 @@
     return apply(itm.tm, v_inner, inner_index...)
 end
 
-function apply_transpose(itm::InflatedTensorMapping{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
+function apply_transpose(itm::InflatedLazyTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg{Any,D}) where {T,R,D}
     dim_before = range_dim(itm.before)
     dim_domain = domain_dim(itm.tm)
     dim_range = range_dim(itm.tm)
@@ -383,7 +383,7 @@
 @doc raw"""
     LazyOuterProduct(tms...)
 
-Creates a `TensorMappingComposition` for the outerproduct of `tms...`.
+Creates a `LazyTensorComposition` for the outerproduct of `tms...`.
 This is done by separating the outer product into regular products of outer products involving only identity mappings and one non-identity mapping.
 
 First let
@@ -419,34 +419,34 @@
 """
 function LazyOuterProduct end
 
-function LazyOuterProduct(tm1::TensorMapping{T}, tm2::TensorMapping{T}) where T
-    itm1 = InflatedTensorMapping(tm1, IdentityMapping{T}(range_size(tm2)))
-    itm2 = InflatedTensorMapping(IdentityMapping{T}(domain_size(tm1)),tm2)
+function LazyOuterProduct(tm1::LazyTensor{T}, tm2::LazyTensor{T}) where T
+    itm1 = InflatedLazyTensor(tm1, IdentityTensor{T}(range_size(tm2)))
+    itm2 = InflatedLazyTensor(IdentityTensor{T}(domain_size(tm1)),tm2)
 
     return itm1∘itm2
 end
 
-LazyOuterProduct(t1::IdentityMapping{T}, t2::IdentityMapping{T}) where T = IdentityMapping{T}(t1.size...,t2.size...)
-LazyOuterProduct(t1::TensorMapping, t2::IdentityMapping) = InflatedTensorMapping(t1, t2)
-LazyOuterProduct(t1::IdentityMapping, t2::TensorMapping) = InflatedTensorMapping(t1, t2)
+LazyOuterProduct(t1::IdentityTensor{T}, t2::IdentityTensor{T}) where T = IdentityTensor{T}(t1.size...,t2.size...)
+LazyOuterProduct(t1::LazyTensor, t2::IdentityTensor) = InflatedLazyTensor(t1, t2)
+LazyOuterProduct(t1::IdentityTensor, t2::LazyTensor) = InflatedLazyTensor(t1, t2)
 
-LazyOuterProduct(tms::Vararg{TensorMapping}) = foldl(LazyOuterProduct, tms)
+LazyOuterProduct(tms::Vararg{LazyTensor}) = foldl(LazyOuterProduct, tms)
 
-⊗(a::TensorMapping, b::TensorMapping) = LazyOuterProduct(a,b)
+⊗(a::LazyTensor, b::LazyTensor) = LazyOuterProduct(a,b)
 
 
-function check_domain_size(tm::TensorMapping, sz)
+function check_domain_size(tm::LazyTensor, sz)
     if domain_size(tm) != sz
         throw(SizeMismatch(tm,sz))
     end
 end
 
 struct SizeMismatch <: Exception
-    tm::TensorMapping
+    tm::LazyTensor
     sz
 end
 
 function Base.showerror(io::IO, err::SizeMismatch)
     print(io, "SizeMismatch: ")
-    print(io, "domain size $(domain_size(err.tm)) of TensorMapping not matching size $(err.sz)")
+    print(io, "domain size $(domain_size(err.tm)) of LazyTensor not matching size $(err.sz)")
 end

--- a/src/LazyTensors/tensor_mapping.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/LazyTensors/tensor_mapping.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,69 +1,69 @@
-export TensorMapping
+export LazyTensor
 export apply
 export apply_transpose
 export range_dim, domain_dim
 export range_size, domain_size
 
 """
-    TensorMapping{T,R,D}
+    LazyTensor{T,R,D}
 
 Describes a mapping of a `D` dimension tensor to an `R` dimension tensor.
 The action of the mapping is implemented through the method
 ```julia
-    apply(t::TensorMapping{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg) where {R,D,T}
+    apply(t::LazyTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg) where {R,D,T}
 ```
 
 The size of the range and domain that the operator works with should be returned by
 the functions
 ```julia
-    range_size(::TensorMapping)
-    domain_size(::TensorMapping)
+    range_size(::LazyTensor)
+    domain_size(::LazyTensor)
 ```
 to allow querying for one or the other.
 
 Optionally the action of the transpose may be defined through
 ```julia
-    apply_transpose(t::TensorMapping{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T}
+    apply_transpose(t::LazyTensor{T,R,D}, v::AbstractArray{T,D}, I::Vararg) where {R,D,T}
 ```
 """
-abstract type TensorMapping{T,R,D} end
+abstract type LazyTensor{T,R,D} end
 
 """
-    apply(t::TensorMapping{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg) where {R,D,T}
+    apply(t::LazyTensor{T,R,D}, v::AbstractArray{<:Any,D}, I::Vararg) where {R,D,T}
 
 Return the result of the mapping for a given index.
 """
 function apply end
 
 """
-    apply_transpose(t::TensorMapping{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg) where {R,D,T}
+    apply_transpose(t::LazyTensor{T,R,D}, v::AbstractArray{<:Any,R}, I::Vararg) where {R,D,T}
 
 Return the result of the transposed mapping for a given index.
 """
 function apply_transpose end
 
 """
-    range_dim(::TensorMapping)
+    range_dim(::LazyTensor)
 Return the dimension of the range space of a given mapping
 """
-range_dim(::TensorMapping{T,R,D}) where {T,R,D} = R
+range_dim(::LazyTensor{T,R,D}) where {T,R,D} = R
 
 """
-    domain_dim(::TensorMapping)
+    domain_dim(::LazyTensor)
 Return the dimension of the domain space of a given mapping
 """
-domain_dim(::TensorMapping{T,R,D}) where {T,R,D} = D
+domain_dim(::LazyTensor{T,R,D}) where {T,R,D} = D
 
 
 """
-    range_size(M::TensorMapping)
+    range_size(M::LazyTensor)
 
 Return the range size for the mapping.
 """
 function range_size end
 
 """
-    domain_size(M::TensorMapping)
+    domain_size(M::LazyTensor)
 
 Return the domain size for the mapping.
 """
@@ -71,10 +71,10 @@
 
 
 """
-    eltype(::TensorMapping{T})
+    eltype(::LazyTensor{T})
 
-The type of elements the TensorMapping acts on.
+The type of elements the LazyTensor acts on.
 """
-Base.eltype(::TensorMapping{T}) where T = T
+Base.eltype(::LazyTensor{T}) where T = T
 
 # TODO: Think about boundschecking!

--- a/src/SbpOperators/boundaryops/boundary_operator.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/boundaryops/boundary_operator.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -6,7 +6,7 @@
 
 When `Dim=1`, the corresponding `BoundaryOperator` tensor mapping is returned.
 When `Dim>1`, the `BoundaryOperator` `op` is inflated by the outer product
-of `IdentityMappings` in orthogonal coordinate directions, e.g for `Dim=3`,
+of `IdentityTensors` in orthogonal coordinate directions, e.g for `Dim=3`,
 the boundary restriction operator in the y-direction direction is `Ix⊗op⊗Iz`.
 """
 function boundary_operator(grid::EquidistantGrid, closure_stencil, boundary::CartesianBoundary)
@@ -17,9 +17,9 @@
     d = dim(boundary)
     op = BoundaryOperator(restrict(grid, d), closure_stencil, r)
 
-    # Create 1D IdentityMappings for each coordinate direction
+    # Create 1D IdentityTensors for each coordinate direction
     one_d_grids = restrict.(Ref(grid), Tuple(1:dimension(grid)))
-    Is = IdentityMapping{eltype(grid)}.(size.(one_d_grids))
+    Is = IdentityTensor{eltype(grid)}.(size.(one_d_grids))
 
     # Formulate the correct outer product sequence of the identity mappings and
     # the boundary operator
@@ -28,15 +28,15 @@
 end
 
 """
-    BoundaryOperator{T,R,N} <: TensorMapping{T,0,1}
+    BoundaryOperator{T,R,N} <: LazyTensor{T,0,1}
 
-Implements the boundary operator `op` for 1D as a `TensorMapping`
+Implements the boundary operator `op` for 1D as a `LazyTensor`
 
 `op` is the restriction of a grid function to the boundary using some closure `Stencil{T,N}`.
 The boundary to restrict to is determined by `R`.
 `op'` is the prolongation of a zero dimensional array to the whole grid using the same closure stencil.
 """
-struct BoundaryOperator{T,R<:Region,N} <: TensorMapping{T,0,1}
+struct BoundaryOperator{T,R<:Region,N} <: LazyTensor{T,0,1}
     stencil::Stencil{T,N}
     size::Int
 end

--- a/src/SbpOperators/boundaryops/boundary_restriction.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/boundaryops/boundary_restriction.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -4,7 +4,7 @@
 """
     boundary_restriction(grid, closure_stencil::Stencil, boundary)
 
-Creates boundary restriction operators `e` as `TensorMapping`s on `boundary`
+Creates boundary restriction operators `e` as `LazyTensor`s on `boundary`
 
 `e` is the restriction of a grid function to `boundary` using a `Stencil` `closure_stencil`.
 `e'` is the prolongation of a grid function on `boundary` to the whole grid using the same `closure_stencil`.

--- a/src/SbpOperators/boundaryops/normal_derivative.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/boundaryops/normal_derivative.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,7 +1,7 @@
 """
     normal_derivative(grid, closure_stencil::Stencil, boundary)
 
-Creates the normal derivative boundary operator `d` as a `TensorMapping`
+Creates the normal derivative boundary operator `d` as a `LazyTensor`
 
 `d` computes the normal derivative of a grid function  on `boundary` a `Stencil` `closure_stencil`.
 `d'` is the prolongation of the normal derivative of a grid function to the whole grid using the same `closure_stencil`.

--- a/src/SbpOperators/volumeops/constant_interior_scaling_operator.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/constant_interior_scaling_operator.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,10 +1,10 @@
 """
-    ConstantInteriorScalingOperator{T,N} <: TensorMapping{T,1,1}
+    ConstantInteriorScalingOperator{T,N} <: LazyTensor{T,1,1}
 
 A one-dimensional operator scaling a vector. The first and last `N` points are
 scaled with individual weights while all interior points are scaled the same.
 """
-struct ConstantInteriorScalingOperator{T,N} <: TensorMapping{T,1,1}
+struct ConstantInteriorScalingOperator{T,N} <: LazyTensor{T,1,1}
     interior_weight::T
     closure_weights::NTuple{N,T}
     size::Int

--- a/src/SbpOperators/volumeops/derivatives/first_derivative.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/derivatives/first_derivative.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,14 +1,14 @@
 """
     first_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
 
-Creates the first-derivative operator `D1` as a `TensorMapping`
+Creates the first-derivative operator `D1` as a `LazyTensor`
 
 `D1` approximates the first-derivative d/dξ on `grid` along the coordinate dimension specified by
 `direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
 for the points in the closure regions.
 
 On a one-dimensional `grid`, `D1` is a `VolumeOperator`. On a multi-dimensional `grid`, `D1` is the outer product of the
-one-dimensional operator with the `IdentityMapping`s in orthogonal coordinate dirrections.
+one-dimensional operator with the `IdentityTensor`s in orthogonal coordinate dirrections.
 
 See also: [`volume_operator`](@ref).
 """

--- a/src/SbpOperators/volumeops/derivatives/second_derivative.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/derivatives/second_derivative.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,14 +1,14 @@
 """
     second_derivative(grid::EquidistantGrid, inner_stencil, closure_stencils, direction)
 
-Creates the second-derivative operator `D2` as a `TensorMapping`
+Creates the second-derivative operator `D2` as a `LazyTensor`
 
 `D2` approximates the second-derivative d²/dξ² on `grid` along the coordinate dimension specified by
 `direction`, using the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`
 for the points in the closure regions.
 
 On a one-dimensional `grid`, `D2` is a `VolumeOperator`. On a multi-dimensional `grid`, `D2` is the outer product of the
-one-dimensional operator with the `IdentityMapping`s in orthogonal coordinate dirrections.
+one-dimensional operator with the `IdentityTensor`s in orthogonal coordinate dirrections.
 
 See also: [`volume_operator`](@ref).
 """

--- a/src/SbpOperators/volumeops/inner_products/inner_product.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/inner_products/inner_product.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,7 +1,7 @@
 """
     inner_product(grid::EquidistantGrid, interior_weight, closure_weights)
 
-Creates the discrete inner product operator `H` as a `TensorMapping` on an
+Creates the discrete inner product operator `H` as a `LazyTensor` on an
 equidistant grid, defined as `(u,v)  = u'Hv` for grid functions `u,v`.
 
 `inner_product` creates `H` on `grid` using the `interior_weight` for the
@@ -11,7 +11,7 @@
 On a 1-dimensional grid, `H` is a `ConstantInteriorScalingOperator`. On a
 N-dimensional grid, `H` is the outer product of the 1-dimensional inner
 product operators for each coordinate direction. On a 0-dimensional grid,
-`H` is a 0-dimensional `IdentityMapping`.
+`H` is a 0-dimensional `IdentityTensor`.
 
 See also: [`ConstantInteriorScalingOperator`](@ref).
 """
@@ -32,7 +32,7 @@
     return H
 end
 
-inner_product(grid::EquidistantGrid{0}, interior_weight, closure_weights) = IdentityMapping{eltype(grid)}()
+inner_product(grid::EquidistantGrid{0}, interior_weight, closure_weights) = IdentityTensor{eltype(grid)}()
 
 """
     inner_product(grid, stencil_set)

--- a/src/SbpOperators/volumeops/inner_products/inverse_inner_product.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/inner_products/inverse_inner_product.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,14 +1,14 @@
 """
     inverse_inner_product(grid::EquidistantGrid, interior_weight, closure_weights)
 
-Constructs the inverse inner product operator `H⁻¹` as a `TensorMapping` using
+Constructs the inverse inner product operator `H⁻¹` as a `LazyTensor` using
 the weights of `H`, `interior_weight`, `closure_weights`. `H⁻¹` is inverse of
 the inner product operator `H`.
 
 On a 1-dimensional grid, `H⁻¹` is a `ConstantInteriorScalingOperator`. On an
 N-dimensional grid, `H⁻¹` is the outer product of the 1-dimensional inverse
 inner product operators for each coordinate direction. On a 0-dimensional
-`grid`, `H⁻¹` is a 0-dimensional `IdentityMapping`. 
+`grid`, `H⁻¹` is a 0-dimensional `IdentityTensor`.
 
 See also: [`ConstantInteriorScalingOperator`](@ref).
 """
@@ -28,7 +28,7 @@
     return H⁻¹
 end
 
-inverse_inner_product(grid::EquidistantGrid{0}, interior_weight, closure_weights) = IdentityMapping{eltype(grid)}()
+inverse_inner_product(grid::EquidistantGrid{0}, interior_weight, closure_weights) = IdentityTensor{eltype(grid)}()
 
 """
     inverse_inner_product(grid, stencil_set)

--- a/src/SbpOperators/volumeops/laplace/laplace.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/laplace/laplace.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -1,11 +1,11 @@
 """
-    Laplace{T, Dim, TM} <: TensorMapping{T, Dim, Dim}
+    Laplace{T, Dim, TM} <: LazyTensor{T, Dim, Dim}
 
 Implements the Laplace operator, approximating ∑d²/xᵢ² , i = 1,...,`Dim` as a
-`TensorMapping`. Additionally `Laplace` stores the stencil set (parsed from TOML) 
-used to construct the `TensorMapping`.
+`LazyTensor`. Additionally `Laplace` stores the stencil set (parsed from TOML)
+used to construct the `LazyTensor`.
 """
-struct Laplace{T, Dim, TM<:TensorMapping{T, Dim, Dim}} <: TensorMapping{T, Dim, Dim}
+struct Laplace{T, Dim, TM<:LazyTensor{T, Dim, Dim}} <: LazyTensor{T, Dim, Dim}
     D::TM       # Difference operator
     stencil_set # Stencil set of the operator
 end
@@ -27,13 +27,13 @@
 LazyTensors.domain_size(L::Laplace) = LazyTensors.domain_size(L.D)
 LazyTensors.apply(L::Laplace, v::AbstractArray, I...) = LazyTensors.apply(L.D,v,I...)
 
-# TODO: Implement pretty printing of Laplace once pretty printing of TensorMappings is implemented. 
+# TODO: Implement pretty printing of Laplace once pretty printing of LazyTensors is implemented.
 # Base.show(io::IO, L::Laplace) = ...
 
 """
     laplace(grid::EquidistantGrid, inner_stencil, closure_stencils)
 
-Creates the Laplace operator operator `Δ` as a `TensorMapping`
+Creates the Laplace operator operator `Δ` as a `LazyTensor`
 
 `Δ` approximates the Laplace operator ∑d²/xᵢ² , i = 1,...,`Dim` on `grid`, using
 the stencil `inner_stencil` in the interior and a set of stencils `closure_stencils`

--- a/src/SbpOperators/volumeops/volume_operator.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/src/SbpOperators/volumeops/volume_operator.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -6,7 +6,7 @@
 the stencils `inner_stencil` and `closure_stencils`. When `Dim=1`, the
 corresponding `VolumeOperator` tensor mapping is returned. When `Dim>1`, the
 returned operator is the appropriate outer product of a one-dimensional
-operators and `IdentityMapping`s, e.g for `Dim=3` the volume operator in the
+operators and `IdentityTensor`s, e.g for `Dim=3` the volume operator in the
 y-direction is `I⊗op⊗I`.
 """
 function volume_operator(grid::EquidistantGrid, inner_stencil, closure_stencils, parity, direction)
@@ -14,9 +14,9 @@
 
     # Create 1D volume operator in along coordinate direction
     op = VolumeOperator(restrict(grid, direction), inner_stencil, closure_stencils, parity)
-    # Create 1D IdentityMappings for each coordinate direction
+    # Create 1D IdentityTensors for each coordinate direction
     one_d_grids = restrict.(Ref(grid), Tuple(1:dimension(grid)))
-    Is = IdentityMapping{eltype(grid)}.(size.(one_d_grids))
+    Is = IdentityTensor{eltype(grid)}.(size.(one_d_grids))
     # Formulate the correct outer product sequence of the identity mappings and
     # the volume operator
     parts = Base.setindex(Is, op, direction)
@@ -27,7 +27,7 @@
     VolumeOperator{T,N,M,K} <: TensorOperator{T,1}
 Implements a one-dimensional constant coefficients volume operator
 """
-struct VolumeOperator{T,N,M,K} <: TensorMapping{T,1,1}
+struct VolumeOperator{T,N,M,K} <: LazyTensor{T,1,1}
     inner_stencil::Stencil{T,N}
     closure_stencils::NTuple{M,Stencil{T,K}}
     size::NTuple{1,Int}

--- a/test/DiffOps/DiffOps_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/DiffOps/DiffOps_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -22,8 +22,8 @@
 #     v[:,2] = [7, 8, 9, 10]
 #     v[:,1] = [10, 11, 12, 13]
 #
-#     @test e_w  isa TensorMapping{T,2,1} where T
-#     @test e_w' isa TensorMapping{T,1,2} where T
+#     @test e_w  isa LazyTensor{T,2,1} where T
+#     @test e_w' isa LazyTensor{T,1,2} where T
 #
 #     @test domain_size(e_w, (3,2)) == (2,)
 #     @test domain_size(e_e, (3,2)) == (2,)
@@ -81,8 +81,8 @@
 #     v∂x = evalOn(g, (x,y)-> 2*x + y)
 #     v∂y = evalOn(g, (x,y)-> 2*(y-1) + x)
 #
-#     @test d_w  isa TensorMapping{T,2,1} where T
-#     @test d_w' isa TensorMapping{T,1,2} where T
+#     @test d_w  isa LazyTensor{T,2,1} where T
+#     @test d_w' isa LazyTensor{T,1,2} where T
 #
 #     @test domain_size(d_w, (3,2)) == (2,)
 #     @test domain_size(d_e, (3,2)) == (2,)

--- a/test/LazyTensors/lazy_tensor_operations_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/LazyTensors/lazy_tensor_operations_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -5,7 +5,7 @@
 using Tullio
 
 @testset "Mapping transpose" begin
-    struct DummyMapping{T,R,D} <: TensorMapping{T,R,D} end
+    struct DummyMapping{T,R,D} <: LazyTensor{T,R,D} end
 
     LazyTensors.apply(m::DummyMapping{T,R}, v, I::Vararg{Any,R}) where {T,R} = :apply
     LazyTensors.apply_transpose(m::DummyMapping{T,R,D}, v, I::Vararg{Any,D}) where {T,R,D} = :apply_transpose
@@ -14,7 +14,7 @@
     LazyTensors.domain_size(m::DummyMapping) = :domain_size
 
     m = DummyMapping{Float64,2,3}()
-    @test m' isa TensorMapping{Float64, 3,2}
+    @test m' isa LazyTensor{Float64, 3,2}
     @test m'' == m
     @test apply(m',zeros(Float64,(0,0)), 0, 0, 0) == :apply_transpose
     @test apply(m'',zeros(Float64,(0,0,0)), 0, 0) == :apply
@@ -25,7 +25,7 @@
 end
 
 @testset "TensorApplication" begin
-    struct SizeDoublingMapping{T,R,D} <: TensorMapping{T,R,D}
+    struct SizeDoublingMapping{T,R,D} <: LazyTensor{T,R,D}
         domain_size::NTuple{D,Int}
     end
 
@@ -108,7 +108,7 @@
     end
 end
 
-@testset "TensorMapping binary operations" begin
+@testset "LazyTensor binary operations" begin
     A = ScalingTensor(2.0, (3,))
     B = ScalingTensor(3.0, (3,))
 
@@ -131,14 +131,14 @@
 end
 
 
-@testset "TensorMappingComposition" begin
+@testset "LazyTensorComposition" begin
     A = rand(2,3)
     B = rand(3,4)
 
     Ã = LazyLinearMap(A, (1,), (2,))
     B̃ = LazyLinearMap(B, (1,), (2,))
 
-    @test Ã∘B̃ isa TensorMappingComposition
+    @test Ã∘B̃ isa LazyTensorComposition
     @test range_size(Ã∘B̃) == (2,)
     @test domain_size(Ã∘B̃) == (4,)
     @test_throws SizeMismatch B̃∘Ã
@@ -164,7 +164,7 @@
     w = rand(3)
 
     @test à isa LazyLinearMap{T,1,1} where T
-    @test à isa TensorMapping{T,1,1} where T
+    @test à isa LazyTensor{T,1,1} where T
     @test range_size(Ã) == (3,)
     @test domain_size(Ã) == (4,)
 
@@ -183,7 +183,7 @@
 
     @test range_size(B̃) == (3,4)
     @test domain_size(B̃) == (2,)
-    @test B̃ isa TensorMapping{T,2,1} where T
+    @test B̃ isa LazyTensor{T,2,1} where T
     @test B̃*ones(2) ≈ B[:,:,1] + B[:,:,2] atol=5e-13
     @test B̃*v ≈ B[:,:,1]*v[1] + B[:,:,2]*v[2] atol=5e-13
 
@@ -193,7 +193,7 @@
 
     @test range_size(B̃) == (4,)
     @test domain_size(B̃) == (3,2)
-    @test B̃ isa TensorMapping{T,1,2} where T
+    @test B̃ isa LazyTensor{T,1,2} where T
     @test B̃*ones(3,2) ≈ B[1,:,1] + B[2,:,1] + B[3,:,1] +
                         B[1,:,2] + B[2,:,2] + B[3,:,2] atol=5e-13
     @test B̃*v ≈ B[1,:,1]*v[1,1] + B[2,:,1]*v[2,1] + B[3,:,1]*v[3,1] +
@@ -205,15 +205,15 @@
 end
 
 
-@testset "IdentityMapping" begin
-    @test IdentityMapping{Float64}((4,5)) isa IdentityMapping{T,2} where T
-    @test IdentityMapping{Float64}((4,5)) isa TensorMapping{T,2,2} where T
-    @test IdentityMapping{Float64}((4,5)) == IdentityMapping{Float64}(4,5)
+@testset "IdentityTensor" begin
+    @test IdentityTensor{Float64}((4,5)) isa IdentityTensor{T,2} where T
+    @test IdentityTensor{Float64}((4,5)) isa LazyTensor{T,2,2} where T
+    @test IdentityTensor{Float64}((4,5)) == IdentityTensor{Float64}(4,5)
 
-    @test IdentityMapping(3,2) isa IdentityMapping{Float64,2}
+    @test IdentityTensor(3,2) isa IdentityTensor{Float64,2}
 
     for sz ∈ [(4,5),(3,),(5,6,4)]
-        I = IdentityMapping{Float64}(sz)
+        I = IdentityTensor{Float64}(sz)
         v = rand(sz...)
         @test I*v == v
         @test I'*v == v
@@ -226,7 +226,7 @@
         @test domain_size(I) == sz
     end
 
-    I = IdentityMapping{Float64}((4,5))
+    I = IdentityTensor{Float64}((4,5))
     v = rand(4,5)
     @inferred (I*v)[3,2]
     @inferred (I'*v)[3,2]
@@ -237,8 +237,8 @@
 
     Ã = rand(4,2)
     A = LazyLinearMap(Ã,(1,),(2,))
-    I1 = IdentityMapping{Float64}(2)
-    I2 = IdentityMapping{Float64}(4)
+    I1 = IdentityTensor{Float64}(2)
+    I2 = IdentityTensor{Float64}(4)
     @test A∘I1 == A
     @test I2∘A == A
     @test I1∘I1 == I1
@@ -249,7 +249,7 @@
 
 @testset "ScalingTensor" begin
     st = ScalingTensor(2.,(3,4))
-    @test st isa TensorMapping{Float64, 2, 2}
+    @test st isa LazyTensor{Float64, 2, 2}
     @test range_size(st) == (3,4)
     @test domain_size(st) == (3,4)
 
@@ -261,8 +261,8 @@
     @inferred (st'*v)[2,2]
 end
 
-@testset "InflatedTensorMapping" begin
-    I(sz...) = IdentityMapping(sz...)
+@testset "InflatedLazyTensor" begin
+    I(sz...) = IdentityTensor(sz...)
 
     Ã = rand(4,2)
     B̃ = rand(4,2,3)
@@ -273,26 +273,26 @@
     C = LazyLinearMap(C̃,(1,),(2,3))
 
     @testset "Constructors" begin
-        @test InflatedTensorMapping(I(3,2), A, I(4)) isa TensorMapping{Float64, 4, 4}
-        @test InflatedTensorMapping(I(3,2), B, I(4)) isa TensorMapping{Float64, 5, 4}
-        @test InflatedTensorMapping(I(3), C, I(2,3)) isa TensorMapping{Float64, 4, 5}
-        @test InflatedTensorMapping(C, I(2,3)) isa TensorMapping{Float64, 3, 4}
-        @test InflatedTensorMapping(I(3), C) isa TensorMapping{Float64, 2, 3}
-        @test InflatedTensorMapping(I(3), I(2,3)) isa TensorMapping{Float64, 3, 3}
+        @test InflatedLazyTensor(I(3,2), A, I(4)) isa LazyTensor{Float64, 4, 4}
+        @test InflatedLazyTensor(I(3,2), B, I(4)) isa LazyTensor{Float64, 5, 4}
+        @test InflatedLazyTensor(I(3), C, I(2,3)) isa LazyTensor{Float64, 4, 5}
+        @test InflatedLazyTensor(C, I(2,3)) isa LazyTensor{Float64, 3, 4}
+        @test InflatedLazyTensor(I(3), C) isa LazyTensor{Float64, 2, 3}
+        @test InflatedLazyTensor(I(3), I(2,3)) isa LazyTensor{Float64, 3, 3}
     end
 
     @testset "Range and domain size" begin
-        @test range_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,4,4)
-        @test domain_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,2,4)
+        @test range_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,4,4)
+        @test domain_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,2,4)
 
-        @test range_size(InflatedTensorMapping(I(3,2), B, I(4))) == (3,2,4,2,4)
-        @test domain_size(InflatedTensorMapping(I(3,2), B, I(4))) == (3,2,3,4)
+        @test range_size(InflatedLazyTensor(I(3,2), B, I(4))) == (3,2,4,2,4)
+        @test domain_size(InflatedLazyTensor(I(3,2), B, I(4))) == (3,2,3,4)
 
-        @test range_size(InflatedTensorMapping(I(3), C, I(2,3))) == (3,4,2,3)
-        @test domain_size(InflatedTensorMapping(I(3), C, I(2,3))) == (3,2,3,2,3)
+        @test range_size(InflatedLazyTensor(I(3), C, I(2,3))) == (3,4,2,3)
+        @test domain_size(InflatedLazyTensor(I(3), C, I(2,3))) == (3,2,3,2,3)
 
-        @inferred range_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,4,4)
-        @inferred domain_size(InflatedTensorMapping(I(3,2), A, I(4))) == (3,2,2,4)
+        @inferred range_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,4,4)
+        @inferred domain_size(InflatedLazyTensor(I(3,2), A, I(4))) == (3,2,2,4)
     end
 
     @testset "Application" begin
@@ -300,47 +300,47 @@
         # The inflated tensor mappings are chosen to preserve, reduce and increase the dimension of the result compared to the input.
         tests = [
             (
-                InflatedTensorMapping(I(3,2), A, I(4)),
+                InflatedLazyTensor(I(3,2), A, I(4)),
                 (v-> @tullio res[a,b,c,d] := Ã[c,i]*v[a,b,i,d]), # Expected result of apply
                 (v-> @tullio res[a,b,c,d] := Ã[i,c]*v[a,b,i,d]), # Expected result of apply_transpose
             ),
             (
-                InflatedTensorMapping(I(3,2), B, I(4)),
+                InflatedLazyTensor(I(3,2), B, I(4)),
                 (v-> @tullio res[a,b,c,d,e] := B̃[c,d,i]*v[a,b,i,e]),
                 (v-> @tullio res[a,b,c,d] := B̃[i,j,c]*v[a,b,i,j,d]),
             ),
             (
-                InflatedTensorMapping(I(3,2), C, I(4)),
+                InflatedLazyTensor(I(3,2), C, I(4)),
                 (v-> @tullio res[a,b,c,d] := C̃[c,i,j]*v[a,b,i,j,d]),
                 (v-> @tullio res[a,b,c,d,e] := C̃[i,c,d]*v[a,b,i,e]),
             ),
             (
-                InflatedTensorMapping(I(3,2), A),
+                InflatedLazyTensor(I(3,2), A),
                 (v-> @tullio res[a,b,c] := Ã[c,i]*v[a,b,i]),
                 (v-> @tullio res[a,b,c] := Ã[i,c]*v[a,b,i]),
             ),
             (
-                InflatedTensorMapping(I(3,2), B),
+                InflatedLazyTensor(I(3,2), B),
                 (v-> @tullio res[a,b,c,d] := B̃[c,d,i]*v[a,b,i]),
                 (v-> @tullio res[a,b,c] := B̃[i,j,c]*v[a,b,i,j]),
             ),
             (
-                InflatedTensorMapping(I(3,2), C),
+                InflatedLazyTensor(I(3,2), C),
                 (v-> @tullio res[a,b,c] := C̃[c,i,j]*v[a,b,i,j]),
                 (v-> @tullio res[a,b,c,d] := C̃[i,c,d]*v[a,b,i]),
             ),
             (
-                InflatedTensorMapping(A,I(4)),
+                InflatedLazyTensor(A,I(4)),
                 (v-> @tullio res[a,b] := Ã[a,i]*v[i,b]),
                 (v-> @tullio res[a,b] := Ã[i,a]*v[i,b]),
             ),
             (
-                InflatedTensorMapping(B,I(4)),
+                InflatedLazyTensor(B,I(4)),
                 (v-> @tullio res[a,b,c] := B̃[a,b,i]*v[i,c]),
                 (v-> @tullio res[a,b] := B̃[i,j,a]*v[i,j,b]),
             ),
             (
-                InflatedTensorMapping(C,I(4)),
+                InflatedLazyTensor(C,I(4)),
                 (v-> @tullio res[a,b] := C̃[a,i,j]*v[i,j,b]),
                 (v-> @tullio res[a,b,c] := C̃[i,a,b]*v[i,c]),
             ),
@@ -365,7 +365,7 @@
         end
 
         @testset "application to other type" begin
-            tm = InflatedTensorMapping(I(3,2), A, I(4))
+            tm = InflatedLazyTensor(I(3,2), A, I(4))
 
             v = rand(ComplexF64, domain_size(tm)...)
             @test (tm*v)[1,2,3,1] isa ComplexF64
@@ -375,7 +375,7 @@
         end
 
         @testset "Inference of application" begin
-            tm = InflatedTensorMapping(I(2,3),ScalingTensor(2.0, (3,2)),I(3,4))
+            tm = InflatedLazyTensor(I(2,3),ScalingTensor(2.0, (3,2)),I(3,4))
             v = rand(domain_size(tm)...)
 
             @inferred apply(tm,v,1,2,3,2,2,4)
@@ -383,14 +383,14 @@
         end
     end
 
-    @testset "InflatedTensorMapping of InflatedTensorMapping" begin
+    @testset "InflatedLazyTensor of InflatedLazyTensor" begin
         A = ScalingTensor(2.0,(2,3))
-        itm = InflatedTensorMapping(I(3,2), A, I(4))
-        @test  InflatedTensorMapping(I(4), itm, I(2)) == InflatedTensorMapping(I(4,3,2), A, I(4,2))
-        @test  InflatedTensorMapping(itm, I(2)) == InflatedTensorMapping(I(3,2), A, I(4,2))
-        @test  InflatedTensorMapping(I(4), itm) == InflatedTensorMapping(I(4,3,2), A, I(4))
+        itm = InflatedLazyTensor(I(3,2), A, I(4))
+        @test  InflatedLazyTensor(I(4), itm, I(2)) == InflatedLazyTensor(I(4,3,2), A, I(4,2))
+        @test  InflatedLazyTensor(itm, I(2)) == InflatedLazyTensor(I(3,2), A, I(4,2))
+        @test  InflatedLazyTensor(I(4), itm) == InflatedLazyTensor(I(4,3,2), A, I(4))
 
-        @test InflatedTensorMapping(I(2), I(2), I(2)) isa InflatedTensorMapping # The constructor should always return its type.
+        @test InflatedLazyTensor(I(2), I(2), I(2)) isa InflatedLazyTensor # The constructor should always return its type.
     end
 end
 
@@ -462,7 +462,7 @@
     C = ScalingTensor(5.0, (3,2))
 
     AB = LazyOuterProduct(A,B)
-    @test AB isa TensorMapping{T,2,2} where T
+    @test AB isa LazyTensor{T,2,2} where T
     @test range_size(AB) == (5,3)
     @test domain_size(AB) == (5,3)
 
@@ -471,7 +471,7 @@
 
     ABC = LazyOuterProduct(A,B,C)
 
-    @test ABC isa TensorMapping{T,4,4} where T
+    @test ABC isa LazyTensor{T,4,4} where T
     @test range_size(ABC) == (5,3,3,2)
     @test domain_size(ABC) == (5,3,3,2)
 
@@ -496,15 +496,15 @@
     @test B̃Ã*v₂ ≈ BAv
 
     @testset "Indentity mapping arguments" begin
-        @test LazyOuterProduct(IdentityMapping(3,2), IdentityMapping(1,2)) == IdentityMapping(3,2,1,2)
+        @test LazyOuterProduct(IdentityTensor(3,2), IdentityTensor(1,2)) == IdentityTensor(3,2,1,2)
 
         Ã = LazyLinearMap(A,(1,),(2,))
-        @test LazyOuterProduct(IdentityMapping(3,2), Ã) == InflatedTensorMapping(IdentityMapping(3,2),Ã)
-        @test LazyOuterProduct(Ã, IdentityMapping(3,2)) == InflatedTensorMapping(Ã,IdentityMapping(3,2))
+        @test LazyOuterProduct(IdentityTensor(3,2), Ã) == InflatedLazyTensor(IdentityTensor(3,2),Ã)
+        @test LazyOuterProduct(Ã, IdentityTensor(3,2)) == InflatedLazyTensor(Ã,IdentityTensor(3,2))
 
-        I1 = IdentityMapping(3,2)
-        I2 = IdentityMapping(4)
-        @test I1⊗Ã⊗I2 == InflatedTensorMapping(I1, Ã, I2)
+        I1 = IdentityTensor(3,2)
+        I2 = IdentityTensor(4)
+        @test I1⊗Ã⊗I2 == InflatedLazyTensor(I1, Ã, I2)
     end
 
 end

--- a/test/LazyTensors/tensor_mapping_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/LazyTensors/tensor_mapping_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -2,7 +2,7 @@
 using Sbplib.LazyTensors
 
 @testset "Generic Mapping methods" begin
-    struct DummyMapping{T,R,D} <: TensorMapping{T,R,D} end
+    struct DummyMapping{T,R,D} <: LazyTensor{T,R,D} end
     LazyTensors.apply(m::DummyMapping{T,R,D}, v, I::Vararg{Any,R}) where {T,R,D} = :apply
     @test range_dim(DummyMapping{Int,2,3}()) == 2
     @test domain_dim(DummyMapping{Int,2,3}()) == 3

--- a/test/SbpOperators/boundaryops/boundary_operator_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/boundaryops/boundary_operator_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -18,18 +18,18 @@
             op_l = BoundaryOperator{Lower}(closure_stencil,size(g_1D)[1])
             @test op_l == BoundaryOperator(g_1D,closure_stencil,Lower())
             @test op_l == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Lower}())
-            @test op_l isa TensorMapping{T,0,1} where T
+            @test op_l isa LazyTensor{T,0,1} where T
 
             op_r = BoundaryOperator{Upper}(closure_stencil,size(g_1D)[1])
             @test op_r == BoundaryOperator(g_1D,closure_stencil,Upper())
             @test op_r == boundary_operator(g_1D,closure_stencil,CartesianBoundary{1,Upper}())
-            @test op_r isa TensorMapping{T,0,1} where T
+            @test op_r isa LazyTensor{T,0,1} where T
         end
 
         @testset "2D" begin
             e_w = boundary_operator(g_2D,closure_stencil,CartesianBoundary{1,Upper}())
-            @test e_w isa InflatedTensorMapping
-            @test e_w isa TensorMapping{T,1,2} where T
+            @test e_w isa InflatedLazyTensor
+            @test e_w isa LazyTensor{T,1,2} where T
         end
     end
     op_l, op_r = boundary_operator.(Ref(g_1D), Ref(closure_stencil), boundary_identifiers(g_1D))

--- a/test/SbpOperators/boundaryops/boundary_restriction_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/boundaryops/boundary_restriction_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -18,20 +18,20 @@
             @test e_l == boundary_restriction(g_1D,stencil_set,CartesianBoundary{1,Lower}())
             @test e_l == BoundaryOperator(g_1D,Stencil{Float64}(e_closure),Lower())
             @test e_l isa BoundaryOperator{T,Lower} where T
-            @test e_l isa TensorMapping{T,0,1} where T
+            @test e_l isa LazyTensor{T,0,1} where T
 
             e_r = boundary_restriction(g_1D,e_closure,CartesianBoundary{1,Upper}())
             @test e_r == boundary_restriction(g_1D,stencil_set,CartesianBoundary{1,Upper}())
             @test e_r == BoundaryOperator(g_1D,Stencil{Float64}(e_closure),Upper())
             @test e_r isa BoundaryOperator{T,Upper} where T
-            @test e_r isa TensorMapping{T,0,1} where T
+            @test e_r isa LazyTensor{T,0,1} where T
         end
 
         @testset "2D" begin
             e_w = boundary_restriction(g_2D,e_closure,CartesianBoundary{1,Upper}())
             @test e_w == boundary_restriction(g_2D,stencil_set,CartesianBoundary{1,Upper}())
-            @test e_w isa InflatedTensorMapping
-            @test e_w isa TensorMapping{T,1,2} where T
+            @test e_w isa InflatedLazyTensor
+            @test e_w isa LazyTensor{T,1,2} where T
         end
     end
 

--- a/test/SbpOperators/boundaryops/normal_derivative_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/boundaryops/normal_derivative_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -16,20 +16,20 @@
             d_l = normal_derivative(g_1D, d_closure, CartesianBoundary{1,Lower}())
             @test d_l == normal_derivative(g_1D, stencil_set, CartesianBoundary{1,Lower}())
             @test d_l isa BoundaryOperator{T,Lower} where T
-            @test d_l isa TensorMapping{T,0,1} where T
+            @test d_l isa LazyTensor{T,0,1} where T
         end
         @testset "2D" begin
             d_w = normal_derivative(g_2D, d_closure, CartesianBoundary{1,Lower}())
             d_n = normal_derivative(g_2D, d_closure, CartesianBoundary{2,Upper}())
-            Ix = IdentityMapping{Float64}((size(g_2D)[1],))
-            Iy = IdentityMapping{Float64}((size(g_2D)[2],))
+            Ix = IdentityTensor{Float64}((size(g_2D)[1],))
+            Iy = IdentityTensor{Float64}((size(g_2D)[2],))
             d_l = normal_derivative(restrict(g_2D,1),d_closure,CartesianBoundary{1,Lower}())
             d_r = normal_derivative(restrict(g_2D,2),d_closure,CartesianBoundary{1,Upper}())
             @test d_w == normal_derivative(g_2D, stencil_set, CartesianBoundary{1,Lower}())
             @test d_w ==  d_l⊗Iy
             @test d_n ==  Ix⊗d_r
-            @test d_w isa TensorMapping{T,1,2} where T
-            @test d_n isa TensorMapping{T,1,2} where T
+            @test d_w isa LazyTensor{T,1,2} where T
+            @test d_n isa LazyTensor{T,1,2} where T
         end
     end
     @testset "Accuracy" begin

--- a/test/SbpOperators/volumeops/derivatives/first_derivative_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/volumeops/derivatives/first_derivative_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -27,15 +27,15 @@
         g₁ = EquidistantGrid(11, 0., 1.)
         g₂ = EquidistantGrid((11,14), (0.,1.), (1.,3.))
         
-        @test first_derivative(g₁, stencil_set, 1) isa TensorMapping{Float64,1,1}
-        @test first_derivative(g₂, stencil_set, 2) isa TensorMapping{Float64,2,2}
+        @test first_derivative(g₁, stencil_set, 1) isa LazyTensor{Float64,1,1}
+        @test first_derivative(g₂, stencil_set, 2) isa LazyTensor{Float64,2,2}
 
         interior_stencil = CenteredStencil(-1,0,1)
         closure_stencils = [Stencil(-1,1, center=1)]
 
-        @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa TensorMapping{Float64,1,1}
+        @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa LazyTensor{Float64,1,1}
         @test first_derivative(g₁, interior_stencil, closure_stencils, 1) isa VolumeOperator
-        @test first_derivative(g₂, interior_stencil, closure_stencils, 2) isa TensorMapping{Float64,2,2}
+        @test first_derivative(g₂, interior_stencil, closure_stencils, 2) isa LazyTensor{Float64,2,2}
     end
 
     @testset "Accuracy conditions" begin

--- a/test/SbpOperators/volumeops/derivatives/second_derivative_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/volumeops/derivatives/second_derivative_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -26,10 +26,10 @@
         @testset "2D" begin
             Dₓₓ = second_derivative(g_2D,inner_stencil,closure_stencils,1)
             D2 = second_derivative(g_1D,inner_stencil,closure_stencils)
-            I = IdentityMapping{Float64}(size(g_2D)[2])
+            I = IdentityTensor{Float64}(size(g_2D)[2])
             @test Dₓₓ == D2⊗I
             @test Dₓₓ == second_derivative(g_2D,stencil_set,1)
-            @test Dₓₓ isa TensorMapping{T,2,2} where T
+            @test Dₓₓ isa LazyTensor{T,2,2} where T
         end
     end
 

--- a/test/SbpOperators/volumeops/inner_products/inner_product_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/volumeops/inner_products/inner_product_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -21,14 +21,14 @@
         @testset "0D" begin
             H = inner_product(EquidistantGrid{Float64}(), quadrature_interior, quadrature_closure)
             @test H == inner_product(EquidistantGrid{Float64}(), stencil_set)
-            @test H == IdentityMapping{Float64}()
-            @test H isa TensorMapping{T,0,0} where T
+            @test H == IdentityTensor{Float64}()
+            @test H isa LazyTensor{T,0,0} where T
         end
         @testset "1D" begin
             H = inner_product(g_1D, quadrature_interior, quadrature_closure)
             @test H == inner_product(g_1D, stencil_set)
             @test H isa ConstantInteriorScalingOperator
-            @test H isa TensorMapping{T,1,1} where T
+            @test H isa LazyTensor{T,1,1} where T
         end
         @testset "2D" begin
             H = inner_product(g_2D, quadrature_interior, quadrature_closure)
@@ -36,7 +36,7 @@
             H_y = inner_product(restrict(g_2D,2), quadrature_interior, quadrature_closure)
             @test H == inner_product(g_2D, stencil_set)
             @test H == H_x⊗H_y
-            @test H isa TensorMapping{T,2,2} where T
+            @test H isa LazyTensor{T,2,2} where T
         end
     end
 

--- a/test/SbpOperators/volumeops/inner_products/inverse_inner_product_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/volumeops/inner_products/inverse_inner_product_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -18,14 +18,14 @@
         @testset "0D" begin
             Hi = inverse_inner_product(EquidistantGrid{Float64}(), quadrature_interior, quadrature_closure)
             @test Hi == inverse_inner_product(EquidistantGrid{Float64}(), stencil_set)
-            @test Hi == IdentityMapping{Float64}()
-            @test Hi isa TensorMapping{T,0,0} where T
+            @test Hi == IdentityTensor{Float64}()
+            @test Hi isa LazyTensor{T,0,0} where T
         end
         @testset "1D" begin
             Hi = inverse_inner_product(g_1D,  quadrature_interior, quadrature_closure)
             @test Hi == inverse_inner_product(g_1D, stencil_set)
             @test Hi isa ConstantInteriorScalingOperator
-            @test Hi isa TensorMapping{T,1,1} where T
+            @test Hi isa LazyTensor{T,1,1} where T
         end
         @testset "2D" begin
             Hi = inverse_inner_product(g_2D, quadrature_interior, quadrature_closure)
@@ -33,7 +33,7 @@
             Hi_y = inverse_inner_product(restrict(g_2D,2), quadrature_interior, quadrature_closure)
             @test Hi == inverse_inner_product(g_2D, stencil_set)
             @test Hi == Hi_x⊗Hi_y
-            @test Hi isa TensorMapping{T,2,2} where T
+            @test Hi isa LazyTensor{T,2,2} where T
         end
     end
 

--- a/test/SbpOperators/volumeops/laplace/laplace_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/volumeops/laplace/laplace_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -17,12 +17,12 @@
         @testset "1D" begin
             Δ = laplace(g_1D, inner_stencil, closure_stencils)
             @test Laplace(g_1D, stencil_set) == Laplace(Δ, stencil_set)
-            @test Laplace(g_1D, stencil_set) isa TensorMapping{T,1,1}  where T
+            @test Laplace(g_1D, stencil_set) isa LazyTensor{T,1,1}  where T
         end
         @testset "3D" begin
             Δ = laplace(g_3D, inner_stencil, closure_stencils)
             @test Laplace(g_3D, stencil_set) == Laplace(Δ,stencil_set)
-            @test Laplace(g_3D, stencil_set) isa TensorMapping{T,3,3} where T
+            @test Laplace(g_3D, stencil_set) isa LazyTensor{T,3,3} where T
         end
     end
 
@@ -70,16 +70,16 @@
     @testset "1D" begin
         Δ = laplace(g_1D, inner_stencil, closure_stencils)
         @test Δ == second_derivative(g_1D, inner_stencil, closure_stencils)
-        @test Δ isa TensorMapping{T,1,1}  where T
+        @test Δ isa LazyTensor{T,1,1}  where T
     end
     @testset "3D" begin
         Δ = laplace(g_3D, inner_stencil, closure_stencils)
-        @test Δ isa TensorMapping{T,3,3} where T
+        @test Δ isa LazyTensor{T,3,3} where T
         Dxx = second_derivative(g_3D, inner_stencil, closure_stencils, 1)
         Dyy = second_derivative(g_3D, inner_stencil, closure_stencils, 2)
         Dzz = second_derivative(g_3D, inner_stencil, closure_stencils, 3)
         @test Δ == Dxx + Dyy + Dzz
-        @test Δ isa TensorMapping{T,3,3} where T
+        @test Δ isa LazyTensor{T,3,3} where T
     end
 end
 

--- a/test/SbpOperators/volumeops/volume_operator_test.jl	Fri Mar 18 20:44:17 2022 +0100
+++ b/test/SbpOperators/volumeops/volume_operator_test.jl	Fri Mar 18 21:14:47 2022 +0100
@@ -22,31 +22,31 @@
             op = VolumeOperator(inner_stencil,closure_stencils,(11,),even)
             @test op == VolumeOperator(g_1D,inner_stencil,closure_stencils,even)
             @test op == volume_operator(g_1D,inner_stencil,closure_stencils,even,1)
-            @test op isa TensorMapping{T,1,1} where T
+            @test op isa LazyTensor{T,1,1} where T
         end
         @testset "2D" begin
             op_x = volume_operator(g_2D,inner_stencil,closure_stencils,even,1)
             op_y = volume_operator(g_2D,inner_stencil,closure_stencils,even,2)
-            Ix = IdentityMapping{Float64}((11,))
-            Iy = IdentityMapping{Float64}((12,))
+            Ix = IdentityTensor{Float64}((11,))
+            Iy = IdentityTensor{Float64}((12,))
             @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy
             @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even)
-            @test op_x isa TensorMapping{T,2,2} where T
-            @test op_y isa TensorMapping{T,2,2} where T
+            @test op_x isa LazyTensor{T,2,2} where T
+            @test op_y isa LazyTensor{T,2,2} where T
         end
         @testset "3D" begin
             op_x = volume_operator(g_3D,inner_stencil,closure_stencils,even,1)
             op_y = volume_operator(g_3D,inner_stencil,closure_stencils,even,2)
             op_z = volume_operator(g_3D,inner_stencil,closure_stencils,even,3)
-            Ix = IdentityMapping{Float64}((11,))
-            Iy = IdentityMapping{Float64}((12,))
-            Iz = IdentityMapping{Float64}((10,))
+            Ix = IdentityTensor{Float64}((11,))
+            Iy = IdentityTensor{Float64}((12,))
+            Iz = IdentityTensor{Float64}((10,))
             @test op_x == VolumeOperator(inner_stencil,closure_stencils,(11,),even)⊗Iy⊗Iz
             @test op_y == Ix⊗VolumeOperator(inner_stencil,closure_stencils,(12,),even)⊗Iz
             @test op_z == Ix⊗Iy⊗VolumeOperator(inner_stencil,closure_stencils,(10,),even)
-            @test op_x isa TensorMapping{T,3,3} where T
-            @test op_y isa TensorMapping{T,3,3} where T
-            @test op_z isa TensorMapping{T,3,3} where T
+            @test op_x isa LazyTensor{T,3,3} where T
+            @test op_y isa LazyTensor{T,3,3} where T
+            @test op_z isa LazyTensor{T,3,3} where T
         end
     end