Rename the category of categories

This commit is contained in:
Frederik Hanghøj Iversen 2018-01-21 15:23:40 +01:00
parent b21c9b7a89
commit 26d210dcc3

View file

@ -63,8 +63,8 @@ module _ { ' : Level} where
postulate ident-l : identity ∘f f f
-- ident-l = lift-eq-functors lem lemmm {!refl!} {!!}
CatCat : Category (lsuc ( ')) ( ')
CatCat =
Cat : Category (lsuc ( ')) ( ')
Cat =
record
{ Object = Category '
; Arrow = Functor
@ -110,13 +110,13 @@ module _ { : Level} (C D : Category ) where
; _⊕_ = _:⊕:_
}
proj₁ : Arrow CatCat :product: C
proj₁ : Arrow Cat :product: C
proj₁ = record { func* = fst ; func→ = fst ; ident = refl ; distrib = refl }
proj₂ : Arrow CatCat :product: D
proj₂ : Arrow Cat :product: D
proj₂ = record { func* = snd ; func→ = snd ; ident = refl ; distrib = refl }
module _ {X : Object (CatCat {} {})} (x₁ : Arrow CatCat X C) (x₂ : Arrow CatCat X D) where
module _ {X : Object (Cat {} {})} (x₁ : Arrow Cat X C) (x₂ : Arrow Cat X D) where
open Functor
-- ident' : {c : Object X} → ((func→ x₁) {dom = c} (𝟙 X) , (func→ x₂) {dom = c} (𝟙 X)) ≡ 𝟙 (catProduct C D)
@ -132,23 +132,23 @@ module _ { : Level} (C D : Category ) where
-- Need to "lift equality of functors"
-- If I want to do this like I do it for pairs it's gonna be a pain.
isUniqL : (CatCat proj₁) x x₁
isUniqL : (Cat proj₁) x x₁
isUniqL = lift-eq-functors refl refl {!!} {!!}
isUniqR : (CatCat proj₂) x x₂
isUniqR : (Cat proj₂) x x₂
isUniqR = lift-eq-functors refl refl {!!} {!!}
isUniq : (CatCat proj₁) x x₁ × (CatCat proj₂) x x₂
isUniq : (Cat proj₁) x x₁ × (Cat proj₂) x x₂
isUniq = isUniqL , isUniqR
uniq : ∃![ x ] ((CatCat proj₁) x x₁ × (CatCat proj₂) x x₂)
uniq : ∃![ x ] ((Cat proj₁) x x₁ × (Cat proj₂) x x₂)
uniq = x , isUniq
instance
isProduct : IsProduct CatCat proj₁ proj₂
isProduct : IsProduct Cat proj₁ proj₂
isProduct = uniq
product : Product { = CatCat} C D
product : Product { = Cat} C D
product = record
{ obj = :product:
; proj₁ = proj₁