Update backlog

This commit is contained in:
Frederik Hanghøj Iversen 2018-03-08 00:54:42 +01:00
parent e43bee6d9f
commit fa9a470875
2 changed files with 18 additions and 2 deletions

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@ -4,6 +4,16 @@ 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
* Functor ✓
* Applicative Functor ✗
@ -11,4 +21,11 @@ Prove postulates in `Cat.Wishlist`
* Monoidal functor ✗
* Tensorial strength ✗
* Category ✓
* Monoidal category ✗
* Monoidal category ✗
* Monad
* Monoidal monad ✓
* Kleisli monad ✓
* Problem 2.3 in voe
* 1st contruction ~ monoidal ✓
* 2nd contruction ~ klesli ✓
* 1st ≃ 2nd ✗

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@ -56,7 +56,6 @@ module _ {A B : Set} {S : Subset (A × B)} (ab : A × B) where
backwards (a' , (a=a' , a'b∈S)) = subst (sym a=a') a'b∈S
fwd-bwd : (x : (a , b) S) (backwards forwards) x x
-- isbijective x = pathJ (λ y x₁ → (backwards ∘ forwards) x ≡ x) {!!} {!!} {!!}
fwd-bwd x = pathJprop (λ y _ y) x
bwd-fwd : (x : Σ[ a' A ] (a , a') Diag A × (a' , b) S)