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formatting fix
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marcinjangrzybowski committed Dec 5, 2023
1 parent 8cd6eeb commit d48cf4b
Showing 1 changed file with 8 additions and 9 deletions.
17 changes: 8 additions & 9 deletions Cubical/Categories/Equivalence/WeakEquivalence.agda
Original file line number Diff line number Diff line change
Expand Up @@ -168,15 +168,14 @@ module _
(transport-fillerExt⁻ (ob≡ b)) j))
λ i j x y
Glue (𝑪'.Hom[ unglue _ x , unglue _ y ])
λ { (j = i0) _ , Hom≃ (isWeakEquivalenceTransportFunctor (mk≡ b)) _ _
;(j = i1) _ , idEquiv _
;(i = i1) _ , _
, isProp→PathP (λ j isPropΠ2 λ x y
isPropIsEquiv (transp (λ i₂
let tr = transp (λ j' ob≡ b (j ∨ (i₂ ∧ j'))) (~ i₂ ∨ j)
in Hom≡ b (i₂ ∨ j) (tr x) (tr y)) j))
(λ _ _ snd (Hom≃ (isWeakEquivalenceTransportFunctor (mk≡ b)) _ _))
(λ _ _ snd (idEquiv _)) j x y }
λ { (j = i0) _ , Hom≃ (isWeakEquivalenceTransportFunctor (mk≡ b)) _ _
;(j = i1) _ , idEquiv _
;(i = i1) _ , _
, isProp→PathP (λ j isPropΠ2 λ x y isPropIsEquiv (transp (λ i₂
let tr = transp (λ j' ob≡ b (j ∨ (i₂ ∧ j'))) (~ i₂ ∨ j)
in Hom≡ b (i₂ ∨ j) (tr x) (tr y)) j))
(λ _ _ snd (Hom≃ (isWeakEquivalenceTransportFunctor (mk≡ b)) _ _))
(λ _ _ snd (idEquiv _)) j x y }

leftInv IsoCategoryPath we = cong₂ weakEquivalence
(Functor≡ (transportRefl ∘f (F-ob (func we)))
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