cat/BACKLOG.md

739 B

Backlog

Prove univalence for various categories

Prove postulates in Cat.Wishlist propHasLevel should be in cubical ntypeCommulative might be there as well.

Define and use Monad≡

Prove that the opposite category is a category.

Prove univalence for the category of

  • sets
  • functors and natural transformations

Prove:

  • isProp (Product ...)

  • isProp (HasProducts ...)

  • Functor ✓

  • Applicative Functor ✗

    • Lax monoidal functor ✗
      • Monoidal functor ✗
    • Tensorial strength ✗
  • Category ✓

    • Monoidal category ✗
  • Monad

    • Monoidal monad ✓
    • Kleisli monad ✓
    • Problem 2.3 in voe
      • 1st contruction ~ monoidal ✓
      • 2nd contruction ~ klesli ✓
        • 1st ≃ 2nd ✗