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Finitely presented categories and functors out of them #518

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merged 8 commits into from
Oct 8, 2021

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@epatters epatters commented Oct 6, 2021

This PR begins to implement the 2-category of categories, functors, and natural transformations, which has been a long-standing omission in Catlab given its central role in category theory. Much remains to be done, but here we have:

  • Data structures for finitely presented categories, based on:
    • Graphs plus path equations
    • Presentation objects
  • Functors out of such categories, based on either vectors or dictionaries
  • Interoperability with existing data structures for free diagrams

The approach here follows the "profunctorial" design we have adopted for modeling Set, with (1) FinCats (finitely presented categories) and FinFunctors between them, (2) arbitrary category @instances in the form of Julia types, and (3) FinDomFunctors going from the former to the latter.

@epatters epatters changed the title Beginnings of the 2-category of categories Finitely presented categories and functors out of them Oct 6, 2021
@epatters epatters merged commit b9a9d18 into AlgebraicJulia:master Oct 8, 2021
@epatters epatters deleted the fincats branch October 8, 2021 18:53
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