fredefox/cat
1
0
Fork 0
Code Issues Pull requests Releases Wiki Activity

[QED] Get equivalence from 3rd formulation

Browse source
This commit is contained in:
Frederik Hanghøj Iversen 2018-04-11 12:46:22 +02:00
parent c23c2716a5
commit 4ff8f155ab
1 changed files with 3 additions and 3 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

6
src/Cat/Category.agda
View file

@ -150,11 +150,11 @@ record RawCategory (ℓa ℓb : Level) : Set (lsuc (ℓa ⊔ ℓb)) where
lem : Σ Object (A ≅_) ≃ Σ Object (A ≡_) lem : Σ Object (A ≅_) ≃ Σ Object (A ≡_)
lem = equivSig {ℓa} {ℓb} {Object} {A ≅_} {_} {A ≡_} (f A) lem = equivSig {ℓa} {ℓb} {Object} {A ≅_} {_} {A ≡_} (f A)
aux : isContr (Σ[ B ∈ Object ] A ≡ B) aux : isContr (Σ Object (A ≡_))
aux = {!Σ Object (A ≡_)!} aux = (A , refl) , (λ y → contrSingl (snd y))
step : isContr (Σ Object (A ≅_)) step : isContr (Σ Object (A ≅_))
step = {!subst {P = isContr} {!!} aux!} step = equivPreservesNType {n = ⟨-2⟩} (Equivalence.symmetry lem) aux
propUnivalent : isProp Univalent propUnivalent : isProp Univalent
propUnivalent a b i = propPi (λ iso → propIsContr) a b i propUnivalent a b i = propPi (λ iso → propIsContr) a b i