Update backlog
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BACKLOG.md
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BACKLOG.md
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@ -4,6 +4,16 @@ Backlog
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Prove univalence for various categories
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Prove postulates in `Cat.Wishlist`
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`propHasLevel` should be in `cubical`
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`ntypeCommulative` might be there as well.
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Define and use Monad≡
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Prove that the opposite category is a category.
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Prove univalence for the category of
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* sets
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* functors and natural transformations
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* Functor ✓
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* Applicative Functor ✗
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@ -11,4 +21,11 @@ Prove postulates in `Cat.Wishlist`
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* Monoidal functor ✗
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* Tensorial strength ✗
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* Category ✓
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* Monoidal category ✗
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* Monoidal category ✗
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* Monad
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* Monoidal monad ✓
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* Kleisli monad ✓
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* Problem 2.3 in voe
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* 1st contruction ~ monoidal ✓
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* 2nd contruction ~ klesli ✓
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* 1st ≃ 2nd ✗
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@ -56,7 +56,6 @@ module _ {A B : Set} {S : Subset (A × B)} (ab : A × B) where
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backwards (a' , (a=a' , a'b∈S)) = subst (sym a=a') a'b∈S
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fwd-bwd : (x : (a , b) ∈ S) → (backwards ∘ forwards) x ≡ x
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-- isbijective x = pathJ (λ y x₁ → (backwards ∘ forwards) x ≡ x) {!!} {!!} {!!}
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fwd-bwd x = pathJprop (λ y _ → y) x
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bwd-fwd : (x : Σ[ a' ∈ A ] (a , a') ∈ Diag A × (a' , b) ∈ S)
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