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Small subcategories #861

Merged
merged 58 commits into from
Oct 20, 2023
Merged

Small subcategories #861

merged 58 commits into from
Oct 20, 2023

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fredrik-bakke
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@fredrik-bakke fredrik-bakke commented Oct 18, 2023

Summary

  • Defines subcategories and proves they contain isomorphism-proofs
  • Defines full maps/functors
  • Defines fully faithful maps/functors
  • Introduces isomorphism induction for categories
  • Defines preunivalent categories
  • Defines full subcategories and show they are categories
  • Defines full subprecategories
  • Singleton induction for propositions
  • Removes duplicate theorems for equivalence induction

There was an embarrassing mistake I introduced a couple of days ago where I defined embeddings of categories to only be embeddings on hom-sets instead of equivalences. That is fixed in this PR. Sorry about that 😬

This PR also leaves some future work. Namely, that fully faithful functors reflect isomorphisms, and that subcategories are indeed categories. I don't know when/if I'll take the time to prove those though, so I prefer if this PR is merged before then.

@fredrik-bakke fredrik-bakke changed the title Subcategories Small subcategories Oct 18, 2023
@fredrik-bakke fredrik-bakke marked this pull request as ready for review October 19, 2023 00:51
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@EgbertRijke EgbertRijke left a comment

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This is an amazing pull request, containing many very nice additions to the library. Very cool!

@EgbertRijke EgbertRijke merged commit c2a4b58 into UniMath:master Oct 20, 2023
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@fredrik-bakke fredrik-bakke deleted the subcategories branch October 20, 2023 10:08
fredrik-bakke added a commit to fredrik-bakke/agda-unimath that referenced this pull request Oct 20, 2023
fredrik-bakke added a commit to fredrik-bakke/agda-unimath that referenced this pull request Oct 20, 2023
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2 participants