diff --git a/Cubical/Categories/Instances/Cat.agda b/Cubical/Categories/Instances/Cat.agda index 3fa88518b..845e113a3 100644 --- a/Cubical/Categories/Instances/Cat.agda +++ b/Cubical/Categories/Instances/Cat.agda @@ -35,46 +35,3 @@ module _ (ℓ ℓ' : Level) where ⋆IdR Cat _ = F-rUnit ⋆Assoc Cat _ _ _ = F-assoc isSetHom Cat {y = _ , isSetObY} = isSetFunctor isSetObY - - - -- isUnivalentCat : isUnivalent Cat - -- isUnivalent.univ isUnivalentCat (C , isSmallC) (C' , isSmallC') = - -- {!!} - - -- where - -- w : Iso (CategoryPath C C') (CatIso Cat (C , isSmallC) (C' , isSmallC')) - -- Iso.fun w = pathToIso ∘ Σ≡Prop (λ _ → isPropIsSet) ∘ CategoryPath.mk≡ - -- Iso.inv w (m , isiso inv sec ret) = ww - -- where - -- obIsom : Iso (C .ob) (C' .ob) - -- Iso.fun obIsom = F-ob m - -- Iso.inv obIsom = F-ob inv - -- Iso.rightInv obIsom = cong F-ob sec ≡$_ - -- Iso.leftInv obIsom = cong F-ob ret ≡$_ - - -- homIsom : (x y : C .ob) → - -- Iso (C .Hom[_,_] x y) - -- (C' .Hom[_,_] (fst (isoToEquiv obIsom) x) - -- (fst (isoToEquiv obIsom) y)) - -- Iso.fun (homIsom x y) = F-hom m - -- Iso.inv (homIsom x y) f = - -- subst2 (C [_,_]) (cong F-ob ret ≡$ x) ((cong F-ob ret ≡$ y)) - -- (F-hom inv f) - - -- Iso.rightInv (homIsom x y) b = - -- -- cong (F-hom m) - -- -- (fromPathP {A = (λ i → Hom[ C , F-ob (ret i) x ] (F-ob (ret i) y))} - -- -- {!!}) ∙ - -- {!!} ∙ - -- λ i → (fromPathP (cong F-hom sec)) i b - -- -- {!!} ∙ λ i → {!sec i .F-hom b!} - -- Iso.leftInv (homIsom x y) a = {!!} - - -- open CategoryPath - -- ww : CategoryPath C C' - -- ob≡ ww = ua (isoToEquiv obIsom) - -- Hom≡ ww = RelPathP _ λ x y → isoToEquiv $ homIsom x y - -- id≡ ww = {!!} - -- ⋆≡ ww = {!!} - -- Iso.rightInv w = {!!} - -- Iso.leftInv w = {!!}