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

Add goals for propositionality of products

Browse source
This commit is contained in:
Frederik Hanghøj Iversen 2018-03-08 10:38:46 +01:00
parent 1ef57a19f4
commit 486238e114
1 changed files with 10 additions and 5 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

15
src/Cat/Category/Product.agda
View file

@ -18,11 +18,13 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
proj₁ : ℂ [ obj , A ] proj₁ : ℂ [ obj , A ]
proj₂ : ℂ [ obj , B ] proj₂ : ℂ [ obj , B ]
-- FIXME Not sure this is actually a proposition - so this name is
-- misleading.
record IsProduct (raw : RawProduct) : Set (ℓa ⊔ ℓb) where record IsProduct (raw : RawProduct) : Set (ℓa ⊔ ℓb) where
open RawProduct raw public open RawProduct raw public
field field
isProduct : ∀ {X : Object} (x₁ : ℂ [ X , A ]) (x₂ : ℂ [ X , B ]) isProduct : ∀ {X : Object} (f : ℂ [ X , A ]) (g : ℂ [ X , B ])
→ ∃![ x ] (ℂ [ proj₁ ∘ x ] ≡ x₁ P.× ℂ [ proj₂ ∘ x ] ≡ x₂) → ∃![ f×g ] (ℂ [ proj₁ ∘ f×g ] ≡ f P.× ℂ [ proj₂ ∘ f×g ] ≡ g)
-- | Arrow product -- | Arrow product
_P[_×_] : ∀ {X} → (π₁ : ℂ [ X , A ]) (π₂ : ℂ [ X , B ]) _P[_×_] : ∀ {X} → (π₁ : ℂ [ X , A ]) (π₂ : ℂ [ X , B ])
@ -56,6 +58,9 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
× ℂ [ g ∘ snd ] × ℂ [ g ∘ snd ]
] ]
module Propositionality where module Propositionality {ℓa ℓb : Level} {ℂ : Category ℓa ℓb} {A B : Category.Object ℂ} where
-- TODO `isProp (Product ...)` propProduct : isProp (Product ℂ A B)
-- TODO `isProp (HasProducts ...)` propProduct = {!!}
propHasProducts : isProp (HasProducts ℂ)
propHasProducts = {!!}