cat/BACKLOG.md

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 ✗