(co)products/(co)equalizers for Fincats and Diagrams

[kris-brown]

Main goal: implement the constructions described in Peschke and Tholen (2020) remark 2.8. This involves developing a lot of other prerequisite functionality.

Main contributions:

• Currying FinDomFunctors into C-Set as FinDomFunctors into Set
• pushout-based chase
  • Collage of functor
  • Conversion between C-Set and SpanC-Set (a model for C-Rel)
  • left kan extensions of FinDomFunctors into Set (or C-Set) + universal property
• Limits/colimits the category of FinCats
• Limits/colimits the category of Diagrams + universal properties
  • Left kan extension used to compute coequalizers for Diagram{id}

To-do:

• Left kan extension to compute equalizers for Diagram{op}
• Universal property of coequalizers (id) / equalizers (op).
• Treatment of equations for (co)equalizers of FinCats

Caveats:

• Code for (co)limits of FinCats is stored in Limits.jl to avoid circular dependency. Tests are still in test/.../FinCats.jl
• For simplicity, FinCatPresentations are treated (but, ideally, code generically would work with FinCatGraphs as well)
• Because of the makeshift way dynamic acsets are implemented, rather than MyCSetType() it's safer to use Base.invokelatest(MyCSetType)
• Left kan extensions are abysmally slow (likely due to the dynamic acset hack)