diff --git a/src/CellArrays.jl b/src/CellArrays.jl
index 6d703e0..c917c86 100644
--- a/src/CellArrays.jl
+++ b/src/CellArrays.jl
@@ -1,6 +1,7 @@
 module CellArrays
 
 using CellwiseValues
+using CellwiseValues.CellValues: _test_iter_cell_value
 
 export CellArray
 export CellMatrix
@@ -50,7 +51,7 @@ collect(a::CellArray) = [ copy(ai) for ai in a ]
 function test_iter_cell_array(
   icv::CellArray{T,N},
   a::AbstractArray{<:AbstractArray{T,N}}) where {T,N}
-  test_iter_cell_value(icv,a)
+  _test_iter_cell_value(icv,a)
 end
 
 function test_index_cell_array(
diff --git a/src/CellMapOperations.jl b/src/CellMapOperations.jl
index d92b9b4..de75956 100644
--- a/src/CellMapOperations.jl
+++ b/src/CellMapOperations.jl
@@ -1,20 +1,27 @@
 module CellMapOperations
 
 using CellwiseValues
+using CellwiseValues.MapOperations: _compute_S, _compute_M
+using CellwiseValues.MapOperations: MapFromKernel
+using CellwiseValues.ArrayOperations: _compute_N, _compute_T
 
 import CellwiseValues: evaluate
-import MapOperations: _stype: _m
+import CellwiseValues.MapOperations: _stype, _m
 import CellwiseValues.ArrayOperations: _nd, _eltype
 import CellwiseValues: apply
 import Base: iterate
 import Base: length
 
+function apply(k::ArrayKernel,m::CellMap,v::Vararg{<:CellValue})
+  CellMapFromKernel(k,m,v...)
+end
+
 struct CellMapFromKernel{S,M,T,N,R,K,V} <: IterCellMap{S,M,T,N,R}
   kernel::K
   cellvalues::V
 end
 
-function CellMapFromKernel(k::ArrayKernel,v::Vararg{<:CellValues})
+function CellMapFromKernel(k::ArrayKernel,v::Vararg{<:CellValue})
   S = _compute_S(v)
   M = _compute_M(v)
   T = _compute_T(k,v)
@@ -70,8 +77,8 @@ function _compute_R(k,v)
   T = _compute_T(k,m)
   N = _compute_N(k,m)
   K = typeof(k)
-  V = m
-  C = tuple([ _cache_type(mi) for mi in m]...)
+  V = Tuple{m...}
+  C = Tuple{[ _cache_type(mi) for mi in m]...}
   MapFromKernel{S,M,T,N,K,V,C}
 end
 
diff --git a/src/CellMaps.jl b/src/CellMaps.jl
index 87edeca..f3881b4 100644
--- a/src/CellMaps.jl
+++ b/src/CellMaps.jl
@@ -2,6 +2,7 @@ module CellMaps
 
 using Test
 using CellwiseValues
+using CellwiseValues.CellValues: _test_iter_cell_value
 
 export CellMap
 export IterCellMap
@@ -9,6 +10,12 @@ export IndexCellMap
 import CellwiseValues: evaluate
 export test_iter_cell_map
 export test_index_cell_map
+export test_index_cell_map_with_index_arg
+
+import Base: iterate
+import Base: length
+import Base: size
+import Base: getindex
 
 """
 Abstract object that traverses a set of cells and at every cell returns a
@@ -26,11 +33,82 @@ Abstract object that for a given cell index returns a `Map{S,M,T,N}`
 """
 const CellMap{S,M,T,N} = Union{IterCellMap{S,M,T,N},IndexCellMap{S,M,T,N}}
 
+# evaluation
+
 """
 Return the cellwise maps of a `CellMap` on a cellwise set of points
 """
-function evaluate(::CellMap{S,M,T,N},::CellArray{S,M})::CellArray{T,N} where {S,M,T,N}
-  @abstractmethod
+function evaluate(cm::CellMap{S,M,T,N},ca::CellArray{S,M}) where {S,M,T,N}
+  IterCellMapValue(cm,ca)
+end
+
+function evaluate(cm::IndexCellMap{S,M,T,N},ca::IndexCellArray{S,M}) where {S,M,T,N}
+  IndexCellMapValue(cm,ca)
+end
+
+struct IterCellMapValue{T,N,V,A} <: IterCellArray{T,N,CachedArray{T,N,Array{T,N}}}
+  cm::V
+  ca::A
+end
+
+function IterCellMapValue(cm::CellMap{S,M,T,N},ca::CellArray{S,M}) where {S,M,T,N}
+  V = typeof(cm)
+  A = typeof(ca)
+  IterCellMapValue{T,N,V,A}(cm,ca)
+end
+
+length(v::IterCellMapValue) = length(v.ca)
+
+@inline function iterate(v::IterCellMapValue{T,N}) where {T,N}
+  cmnext = iterate(v.cm)
+  canext = iterate(v.ca)
+  r = CachedArray(T,N)
+  _iterate(cmnext,canext,r)
+end
+
+@inline function iterate(v::IterCellMapValue,state)
+  cmstate, castate, r = state
+  cmnext = iterate(v.cm,cmstate)
+  canext = iterate(v.ca,castate)
+  _iterate(cmnext,canext,r)
+end
+
+@inline function _iterate(cmnext,canext,r)
+  if cmnext === nothing; return nothing end
+  if canext === nothing; return nothing end
+  m, cmstate = cmnext
+  a, castate = canext
+  s = return_size(m,size(a))
+  setsize!(r,s)
+  evaluate!(m,a,r)
+  state = (cmstate,castate,r)
+  (r, state)
+end
+
+struct IndexCellMapValue{T,N,V,A} <: IndexCellArray{T,N,CachedArray{T,N,Array{T,N}},1}
+  cm::V
+  ca::A
+  r::CachedArray{T,N,Array{T,N}}
+end
+
+function IndexCellMapValue(cm::IndexCellMap{S,M,T,N},ca::IndexCellArray{S,M}) where {S,M,T,N}
+  V = typeof(cm)
+  A = typeof(ca)
+  r = CachedArray(T,N)
+  IndexCellMapValue{T,N,V,A}(cm,ca,r)
+end
+
+length(v::IndexCellMapValue) = length(v.ca)
+
+size(v::IndexCellMapValue) = (length(v),)
+
+function getindex(v::IndexCellMapValue,i::Integer)
+  m = v.cm[i]
+  a = v.ca[i]
+  s = return_size(m,size(a))
+  setsize!(v.r,s)
+  evaluate!(m,a,v.r)
+  v.r
 end
 
 # Testers
@@ -44,7 +122,7 @@ function test_iter_cell_map(
   @test length(m) == length(a)
 
   c = evaluate(m,a)
-  test_iter_cell_array(c,b)
+  _test_iter_cell_value(c,b)
 
   for (mi,ai,bi) in zip(m,a,b)
     @assert isa(mi,Map{S,M,T,N})
@@ -73,4 +151,34 @@ function test_index_cell_map(
 
 end
 
+function test_index_cell_map_with_index_arg(
+  m::IndexCellMap{S,M,T,N},
+  a::IndexCellArray{S,M},
+  b::AbstractArray{<:AbstractArray{T,N}}) where {S,M,T,N}
+
+  test_index_cell_map(m,a,b)
+
+  c = evaluate(m,a)
+  @test isa(c,IndexCellArray)
+
+  @test length(c) == length(m)
+  @test length(c) == length(a)
+
+  for i in 1:length(c)
+    mi = m[i]
+    bi = b[i]
+    ci = c[i]
+    @assert bi ≈ ci
+  end
+
+  for i in 1:length(m)
+    mi = m[i]
+    ai = a[i]
+    bi = b[i]
+    @assert isa(mi,Map{S,M,T,N})
+    @assert evaluate(mi,ai) ≈ bi
+  end
+
+end
+
 end # module CellMaps
diff --git a/src/CellValues.jl b/src/CellValues.jl
index 413e52f..e65dbcc 100644
--- a/src/CellValues.jl
+++ b/src/CellValues.jl
@@ -57,6 +57,10 @@ end
 # Testers
 
 function test_iter_cell_value(icv::CellValue{T},a::AbstractArray{T}) where T
+  _test_iter_cell_value(icv,a)
+end
+
+function _test_iter_cell_value(icv,a)
 
   @test length(icv) == length(a)
 
diff --git a/src/CellwiseValues.jl b/src/CellwiseValues.jl
index 9ff354c..2e8d8d9 100644
--- a/src/CellwiseValues.jl
+++ b/src/CellwiseValues.jl
@@ -5,6 +5,9 @@ using Reexport
 include("Helpers.jl")
 @reexport using CellwiseValues.Helpers
 
+include("CachedArrays.jl")
+@reexport using CellwiseValues.CachedArrays
+
 include("CellValues.jl")
 @reexport using CellwiseValues.CellValues
 
@@ -29,9 +32,6 @@ include("Kernels.jl")
 include("NumberOperations.jl")
 @reexport using CellwiseValues.NumberOperations
 
-include("CachedArrays.jl")
-@reexport using CellwiseValues.CachedArrays
-
 include("ArrayOperations.jl")
 @reexport using CellwiseValues.ArrayOperations
 
diff --git a/test/CellMapOperationsTests.jl b/test/CellMapOperationsTests.jl
index e69de29..f91306b 100644
--- a/test/CellMapOperationsTests.jl
+++ b/test/CellMapOperationsTests.jl
@@ -0,0 +1,50 @@
+include("CellValuesMocks.jl")
+include("MapsMocks.jl")
+include("../src/CellMapOperations.jl")
+module CellMapOperationsTests
+
+using Test
+using CellwiseValues
+using TensorValues
+
+using ..CellValuesMocks
+using ..MapsMocks
+
+l = 10
+
+a = VectorValue(10,10)
+b = VectorValue(15,20)
+p1 = VectorValue(1,1)
+p2 = VectorValue(2,2)
+p3 = VectorValue(3,3)
+p = [p1,p2,p3]
+m = MockMap(a)
+r = evaluate(m,p)
+
+cm = TestIterCellValue(m,l)
+cp = TestIterCellValue(p,l)
+rm = [ CachedArray(r) for i in 1:l]
+
+test_iter_cell_map(cm,cp,rm)
+
+cm2 = apply(-,cm,broadcast=true)
+rm = [ CachedArray(-r) for i in 1:l]
+
+@test length(cm2) == length(cm)
+@test length(cm2) == length(rm)
+
+test_iter_cell_map(cm2,cp,rm)
+
+
+
+cm = TestIndexCellValue(m,l)
+cp = TestIndexCellValue(p,l)
+rm = [ CachedArray(r) for i in 1:l]
+
+test_index_cell_map_with_index_arg(cm,cp,rm)
+
+ca2 = evaluate(cm,cp)
+
+test_index_cell_array(ca2,rm)
+
+end # module CellMapOperationsTests
diff --git a/test/CellMapsTests.jl b/test/CellMapsTests.jl
new file mode 100644
index 0000000..7b6d296
--- /dev/null
+++ b/test/CellMapsTests.jl
@@ -0,0 +1,31 @@
+module CellMapsTests
+
+using Test
+using CellwiseValues
+using TensorValues
+
+using ..CellValuesMocks
+using ..MapsMocks
+
+l = 10
+
+a = VectorValue(10,10)
+b = VectorValue(15,20)
+p1 = VectorValue(1,1)
+p2 = VectorValue(2,2)
+p3 = VectorValue(3,3)
+p = [p1,p2,p3]
+m = MockMap(a)
+r = evaluate(m,p)
+
+cm = TestIterCellValue(m,l)
+cp = TestIterCellValue(p,l)
+rm = [ CachedArray(r) for i in 1:l]
+test_iter_cell_map(cm,cp,rm)
+
+cm = TestIndexCellValue(m,l)
+cp = TestIndexCellValue(p,l)
+rm = [ CachedArray(r) for i in 1:l]
+test_index_cell_map_with_index_arg(cm,cp,rm)
+
+end # module CellMapsTests
diff --git a/test/CellValuesMocks.jl b/test/CellValuesMocks.jl
index 0805b64..35c4e50 100644
--- a/test/CellValuesMocks.jl
+++ b/test/CellValuesMocks.jl
@@ -8,6 +8,7 @@ import Base: iterate
 import Base: length
 import Base: size
 import Base: getindex
+import CellwiseValues: evaluate
 
 struct TestIndexCellValue{T} <: IndexCellValue{T,1}
   a::T