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Adjoints preserve diagrams #455

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Taneb
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@Taneb Taneb commented Feb 26, 2025

Supersedes #454 and, to me, justifies removing Categories.Adjoint.Equivalence.Properties entirely, as ⊣equiv-preserves-diagram is a special case of la-preserves-diagram (along with sym).

The proof is mostly the same as in Categories.Adjoint.Equivalence.Properties, apart from !cone.commute, which takes a different route. (I suspect the author of that module seeing that proof before this proof was what led them to believe the equivalence was necessary)

Discussion points:

  • Are these names good enough?
  • Is this the right module to put these laws in?
  • Should we remove Categories.Adjoint.Equivalence.Properties now?
  • What should we do about the comment in Categories.Category.Finite?

@JacquesCarette
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  • do we use 'la' and 'ra' anywhere else? I think I've seen LAdj and RAdj?
  • yes
  • yes
  • they probably need a thorough review. I've never been fully convinced with that definition (but I'm still searching for a good definition of Finite, so it's deeper than just this code, which wasn't mine.)

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