Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

(C ≃ᶜ C') ≃ (C ≡ C') & univalent category of setoids #1084

Closed

Conversation

marcinjangrzybowski
Copy link
Contributor

new modules:

  • Cubical/Categories/Category/Path.agda -
    Simple helper representation of Path between categories to deal with ineficiency in WeakEquivalence.agda
  • Cubical/Relation/Binary/Setoid.agda Setoid -
    Pair of hSet and propositional equivalence relation
  • Cubical/Categories/Instances/Setoids.agda -
    Univalent Category of Setoids with adjoint quadruple of functors from/to SET : Quot ⊣ IdRel ⊣ Forget ⊣ FullRel

additions:

  • Cubical/Categories/Adjoint.agda - added composiiton of adjunctions
  • Cubical/Categories/Equivalence/WeakEquivalence.agda - Equivalence of Categories is equivalent to Path between Univalent Categories
  • Cubical/Categories/Instances/Functors.agda - currying of functors is an isomorphism.
  • Cubical/Foundations/Transport.agda - transport-filler-ua = ua-gluePath
  • some other minor helpers

* Cubical/Categories/Category/Path.agda
  Helper representation of Path between categories to deal with ineficiency in WeakEquivalence.agda
* Cubical/Relation/Binary/Setoid.agda
  Setoid - Pair of hSet and propositional equivalence relation
* Cubical/Categories/Instances/Setoids.agda
  Univalent Category of Setoids

changes:
* Cubical/Categories/Adjoint.agda
  added composiiton of adjunctions
* Cubical/Categories/Equivalence/WeakEquivalence.agda
  Equivalence equivalent to Path for Univalent Categories
* Cubical/Categories/Instances/Functors.agda
  currying of functors is an isomorphism.
* Cubical/Foundations/Transport.agda
  transport-filler-ua = ua-gluePath

+ some other minor helpers
@marcinjangrzybowski
Copy link
Contributor Author

I will reopen after spliting into more generic categorical stuff vs relations stuff vs setoids

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
Labels
None yet
Projects
None yet
Development

Successfully merging this pull request may close these issues.

1 participant