Replace manual functor application with FinDomFunctor composition

[Copilot]

The mesh decomposition docs were manually iterating over diagram objects and morphisms to apply FMatPushforward, when Catlab provides FinDomFunctor for automatic functor composition.

Changes

Before (manual iteration, 8 lines):

vect_obs = [length(ob) for ob in diag[:ob]]
vect_homs = [(hom_map(FMatPushforward, diag[e, :hom]), diag[e, :src], diag[e, :tgt]) 
             for e in edges(diag)]
Vdiag = FreeGraph(vect_obs, vect_homs)

After (functor composition, 1 line):

Vdiag = force(compose(FinDomFunctor(diag), FMatPushforward))

FinDomFunctor converts the diagram to a functor, compose performs categorical composition, and force evaluates the result. No explicit iteration required.

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Original prompt

---

This section details on the original issue you should resolve

<issue_title>Resolve failing blocks in mesh decomposition docs page</issue_title>
<issue_description>Certain blocks are failing in the mesh decomposition blocks page.
https://github.com/AlgebraicJulia/CombinatorialSpaces.jl/actions/runs/21646942255/job/62401267914</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Resolve failing blocks in mesh decomposition docs page #194

---

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[lukem12345]

│ Vdiag = force(compose(FinDomFunctor(diag), FMatPushforward))
│
│   exception =
│    MethodError: no method matching ob_map(::Catlab.CategoricalAlgebra.Cats.Functors.Functor{Catlab.BasicSets.FinSets.FinSet, Catlab.BasicSets.FinSets.FinSet, Catlab.BasicSets.FinFunctions.FinFunction, Function}, ::Catlab.BasicSets.SumSets.TaggedElem{Val{:Ob}, Nothing})
│    The function `ob_map` exists, but no method is defined for this combination of argument types.

[lukem12345]

│ Vdiag = force(compose[Category(FinVect())](FinDomFunctor(diag), FMatPushforward))
│ ```
│ exception =
│ MethodError: no method matching compose(::GATlab.Syntax.TheoryInterface.WithModel{Catlab.CategoricalAlgebra.Cats.Categories.Category}, ::Catlab.CategoricalAlgebra.Cats.FinFunctors.FinDomFunctor{Union{Catlab.Theories.FreeSchema.AttrType{:generator}, Catlab.Theories.FreeSchema.Ob{:generator}}, Union{Catlab.BasicSets.SumSets.TaggedElem{Val{:Ob}, Nothing}, Catlab.BasicSets.SumSets.TaggedElem{Val{:Hom}, Nothing}, Catlab.BasicSets.FinSetInts.FinSetInt}, Union{Catlab.Theories.FreeSchema.Attr, Catlab.Theories.FreeSchema.Hom}, Union{Catlab.BasicSets.SumSets.TaggedElem{Val{:Ob}, Nothing}, Catlab.BasicSets.SumSets.TaggedElem{Val{:Hom}, Nothing}, Catlab.BasicSets.FinFunctions.FinFunction, Catlab.BasicSets.SumSets.TaggedElem{Val{:Ob}, Catlab.BasicSets.FinDomFunctions.FinDomFunction}, Catlab.BasicSets.SumSets.TaggedElem{Val{:Hom}, Catlab.BasicSets.FinDomFunctions.FinDomFunction}}, Union{Catlab.Theories.FreeSchema.Attr{:generator}, Catlab.Theories.FreeSchema.Hom{:generator}}}, ::Catlab.CategoricalAlgebra.Cats.Functors.Functor{Catlab.BasicSets.FinSets.FinSet, Catlab.BasicSets.FinSets.FinSet, Catlab.BasicSets.FinFunctions.FinFunction, Function}; context::Nothing)

[lukem12345]

Looking at the docs build for the original mesh decomposition PR.

Introduced here: fd90df4

Formatting of codeblocks updated in the next commit gets the action to return a ✅, but that’s just a signal that the build finished, not that no blocks contained errors.
fd90df4

Associated action:
https://github.com/AlgebraicJulia/CombinatorialSpaces.jl/actions/runs/20467878719/job/58815995340

As it stands, I’m not sure what the code here is meant to do in Catlab 0.17 . Looking at this comment in the source code for sheaves:
https://github.com/AlgebraicJulia/Catlab.jl/blob/6d03f3570b453ca5995baca3a920bd2a21897052/src/sheaves/FVect.jl#L5

The tests do not currently use the category structure of FinVect

Maybe I should just delete this block and wait for Catlab.Sheaves and the category of FinVect to be integrated more deeply with the rest of the codebase?

[lukem12345]

@quffaro I assume that I am just supposed to update Vdiag = force(compose[Category(FinVect())](FinDomFunctor(diag), FMatPushforward)) with the appropriate category for the compose call. Does that seem right?

I’m reading through the tests and these all sound like possible candidates:

• SkelFinSet()
• Category(SetC())
• FinCat(something)
• Category(DiscreteFinCat(FinSet(something)))
• FinSetC()
  There’s also FinVect which is not used in the tests.