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Make parameters explicit

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Frederik Hanghøj Iversen 2018-03-08 10:22:21 +01:00
parent fae492a1e3
commit faf4c54188
3 changed files with 11 additions and 9 deletions
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4
src/Cat/Categories/Cat.agda
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@ -151,7 +151,7 @@ module _ {ℓ ℓ' : Level} (unprovable : IsCategory (RawCat ℓ ℓ')) where
private private
module P = CatProduct ℂ 𝔻 module P = CatProduct ℂ 𝔻
rawProduct : RawProduct {ℂ = Catℓ} ℂ 𝔻 rawProduct : RawProduct Catℓ ℂ 𝔻
RawProduct.obj rawProduct = P.obj RawProduct.obj rawProduct = P.obj
RawProduct.proj₁ rawProduct = P.proj₁ RawProduct.proj₁ rawProduct = P.proj₁
RawProduct.proj₂ rawProduct = P.proj₂ RawProduct.proj₂ rawProduct = P.proj₂
@ -159,7 +159,7 @@ module _ {ℓ ℓ' : Level} (unprovable : IsCategory (RawCat ℓ ℓ')) where
isProduct : IsProduct Catℓ rawProduct isProduct : IsProduct Catℓ rawProduct
IsProduct.isProduct isProduct = P.isProduct IsProduct.isProduct isProduct = P.isProduct
product : Product {ℂ = Catℓ} ℂ 𝔻 product : Product Catℓ ℂ 𝔻
Product.raw product = rawProduct Product.raw product = rawProduct
Product.isProduct product = isProduct Product.isProduct product = isProduct

6
src/Cat/Categories/Sets.agda
View file

@ -64,15 +64,17 @@ module _ {ℓ : Level} where
lem : proj₁ Function.∘′ (f &&& g) ≡ f × proj₂ Function.∘′ (f &&& g) ≡ g lem : proj₁ Function.∘′ (f &&& g) ≡ f × proj₂ Function.∘′ (f &&& g) ≡ g
proj₁ lem = refl proj₁ lem = refl
proj₂ lem = refl proj₂ lem = refl
rawProduct : RawProduct {ℂ = 𝓢} 0A 0B
rawProduct : RawProduct 𝓢 0A 0B
RawProduct.obj rawProduct = 0A×0B RawProduct.obj rawProduct = 0A×0B
RawProduct.proj₁ rawProduct = Data.Product.proj₁ RawProduct.proj₁ rawProduct = Data.Product.proj₁
RawProduct.proj₂ rawProduct = Data.Product.proj₂ RawProduct.proj₂ rawProduct = Data.Product.proj₂
isProduct : IsProduct 𝓢 rawProduct isProduct : IsProduct 𝓢 rawProduct
IsProduct.isProduct isProduct {X = X} f g IsProduct.isProduct isProduct {X = X} f g
= (f &&& g) , lem {0X = X} f g = (f &&& g) , lem {0X = X} f g
product : Product {ℂ = 𝓢} 0A 0B product : Product 𝓢 0A 0B
Product.raw product = rawProduct Product.raw product = rawProduct
Product.isProduct product = isProduct Product.isProduct product = isProduct

10
src/Cat/Category/Product.agda
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@ -9,14 +9,14 @@ open import Cat.Category hiding (module Propositionality)
open Category open Category
module _ {ℓa ℓb : Level} where module _ {ℓa ℓb : Level} where
record RawProduct {ℂ : Category ℓa ℓb} (A B : Object ℂ) : Set (ℓa ⊔ ℓb) where record RawProduct (ℂ : Category ℓa ℓb) (A B : Object ℂ) : Set (ℓa ⊔ ℓb) where
no-eta-equality no-eta-equality
field field
obj : Object ℂ obj : Object ℂ
proj₁ : ℂ [ obj , A ] proj₁ : ℂ [ obj , A ]
proj₂ : ℂ [ obj , B ] proj₂ : ℂ [ obj , B ]
record IsProduct (ℂ : Category ℓa ℓb) {A B : Object ℂ} (raw : RawProduct {ℂ = ℂ} A B) : Set (ℓa ⊔ ℓb) where record IsProduct (ℂ : Category ℓa ℓb) {A B : Object ℂ} (raw : RawProduct ℂ A B) : Set (ℓa ⊔ ℓb) where
open RawProduct raw public open RawProduct raw public
field field
isProduct : ∀ {X : Object ℂ} (x₁ : ℂ [ X , A ]) (x₂ : ℂ [ X , B ]) isProduct : ∀ {X : Object ℂ} (x₁ : ℂ [ X , A ]) (x₂ : ℂ [ X , B ])
@ -27,16 +27,16 @@ module _ {ℓa ℓb : Level} where
→ ℂ [ X , obj ] → ℂ [ X , obj ]
_P[_×_] π₁ π₂ = P.proj₁ (isProduct π₁ π₂) _P[_×_] π₁ π₂ = P.proj₁ (isProduct π₁ π₂)
record Product {ℂ : Category ℓa ℓb} (A B : Object ℂ) : Set (ℓa ⊔ ℓb) where record Product (ℂ : Category ℓa ℓb) (A B : Object ℂ) : Set (ℓa ⊔ ℓb) where
field field
raw : RawProduct {ℂ = ℂ} A B raw : RawProduct ℂ A B
isProduct : IsProduct ℂ {A} {B} raw isProduct : IsProduct ℂ {A} {B} raw
open IsProduct isProduct public open IsProduct isProduct public
record HasProducts (ℂ : Category ℓa ℓb) : Set (ℓa ⊔ ℓb) where record HasProducts (ℂ : Category ℓa ℓb) : Set (ℓa ⊔ ℓb) where
field field
product : ∀ (A B : Object ℂ) → Product {ℂ = ℂ} A B product : ∀ (A B : Object ℂ) → Product ℂ A B
module _ (A B : Object ℂ) where module _ (A B : Object ℂ) where
open Product (product A B) open Product (product A B)