Commit 2021-01-07 21:43 4da83134

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feat(category_theory/closed): golf definition and proofs (#5623) Using the new mates framework, simplify the definition of pre and shorten proofs about it. To be more specific,

  • pre is now explicitly a natural transformation, rather than indexed morphisms with a naturality property
  • The new definition of pre means things like pre_map which I complained about before are easier to prove, and pre_post_comm is automatic
  • There are now more lemmas relating pre to coev, ev and uncurry: uncurry_pre in particular was a hole in the API.
  • internal_hom has a shorter construction. In particular I changed the type to Cᵒᵖ ⥤ C ⥤ C, which I think is better since the usual external hom functor is given as Cᵒᵖ ⥤ C ⥤ Type*, so this is consistent with that. In a subsequent PR I'll do the same for exp_comparison, but that's a bigger change with improved API so they're separate for now.

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