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Frederik Hanghøj Iversen 2018-04-13 15:26:46 +02:00
parent 7b45b5cdc3
commit 6b7d66b7fc
1 changed files with 3 additions and 6 deletions
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9
src/Cat/Category/Product.agda
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@ -122,8 +122,7 @@ module Try0 {ℓa ℓb : Level} {ℂ : Category ℓa ℓb}
} }
module _ where module _ where
private open RawCategory raw
open RawCategory raw
propEqs : ∀ {X' : Object}{Y' : Object} (let X , xa , xb = X') (let Y , ya , yb = Y') propEqs : ∀ {X' : Object}{Y' : Object} (let X , xa , xb = X') (let Y , ya , yb = Y')
→ (xy : ℂ.Arrow X Y) → isProp (ℂ [ ya ∘ xy ] ≡ xa × ℂ [ yb ∘ xy ] ≡ xb) → (xy : ℂ.Arrow X Y) → isProp (ℂ [ ya ∘ xy ] ≡ xa × ℂ [ yb ∘ xy ] ≡ xb)
@ -262,13 +261,11 @@ module Try0 {ℓa ℓb : Level} {ℂ : Category ℓa ℓb}
helper : PathP (λ i → pA i) xa ya helper : PathP (λ i → pA i) xa ya
helper = coe-lem-inv k1 helper = coe-lem-inv k1
in iso , coe-lem-inv k1 , coe-lem-inv k0}) in iso , coe-lem-inv k1 , coe-lem-inv k0})
, record , funExt (λ x → lemSig
{ fst = funExt (λ x → lemSig
(λ x → propSig prop0 (λ _ → prop1)) (λ x → propSig prop0 (λ _ → prop1))
_ _ _ _
(Σ≡ refl (ℂ.propIsomorphism _ _ _))) (Σ≡ refl (ℂ.propIsomorphism _ _ _)))
; snd = funExt (λ{ (f , _) → lemSig propIsomorphism _ _ (Σ≡ refl (propEqs _ _ _))}) , funExt (λ{ (f , _) → lemSig propIsomorphism _ _ (Σ≡ refl (propEqs _ _ _))})
}
where where
prop0 : ∀ {x} → isProp (PathP (λ i → ℂ.Arrow (ℂ.isoToId x i) A) xa ya) prop0 : ∀ {x} → isProp (PathP (λ i → ℂ.Arrow (ℂ.isoToId x i) A) xa ya)
prop0 {x} = pathJ (λ y p → ∀ x → isProp (PathP (λ i → ℂ.Arrow (p i) A) xa x)) (λ x → ℂ.arrowsAreSets _ _) Y (ℂ.isoToId x) ya prop0 {x} = pathJ (λ y p → ∀ x → isProp (PathP (λ i → ℂ.Arrow (p i) A) xa x)) (λ x → ℂ.arrowsAreSets _ _) Y (ℂ.isoToId x) ya