Rename the category of categories
This commit is contained in:
parent
b21c9b7a89
commit
26d210dcc3
|
@ -63,8 +63,8 @@ module _ {ℓ ℓ' : Level} where
|
|||
postulate ident-l : identity ∘f f ≡ f
|
||||
-- ident-l = lift-eq-functors lem lemmm {!refl!} {!!}
|
||||
|
||||
CatCat : Category (lsuc (ℓ ⊔ ℓ')) (ℓ ⊔ ℓ')
|
||||
CatCat =
|
||||
Cat : Category (lsuc (ℓ ⊔ ℓ')) (ℓ ⊔ ℓ')
|
||||
Cat =
|
||||
record
|
||||
{ Object = Category ℓ ℓ'
|
||||
; Arrow = Functor
|
||||
|
@ -110,13 +110,13 @@ module _ {ℓ : Level} (C D : Category ℓ ℓ) 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 {ℓ} {ℓ})} (x₁ : Arrow CatCat X C) (x₂ : Arrow CatCat X D) where
|
||||
module _ {X : Object (Cat {ℓ} {ℓ})} (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 _ {ℓ : Level} (C D : Category ℓ ℓ) 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 {ℂ = CatCat} C D
|
||||
product : Product {ℂ = Cat} C D
|
||||
product = record
|
||||
{ obj = :product:
|
||||
; proj₁ = proj₁
|
||||
|
|
Loading…
Reference in a new issue