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Factor out objects

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Frederik Hanghøj Iversen 2018-03-08 10:28:05 +01:00
parent 181bd1af53
commit 4e7b350188
3 changed files with 23 additions and 22 deletions
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2
src/Cat/Categories/Cat.agda
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@ -156,7 +156,7 @@ module _ {ℓ ℓ' : Level} (unprovable : IsCategory (RawCat ℓ ℓ')) where
RawProduct.proj₁ rawProduct = P.proj₁ RawProduct.proj₁ rawProduct = P.proj₁
RawProduct.proj₂ rawProduct = P.proj₂ RawProduct.proj₂ rawProduct = P.proj₂
isProduct : IsProduct Catℓ rawProduct isProduct : IsProduct Catℓ _ _ rawProduct
IsProduct.isProduct isProduct = P.isProduct IsProduct.isProduct isProduct = P.isProduct
product : Product Catℓ ℂ 𝔻 product : Product Catℓ ℂ 𝔻

2
src/Cat/Categories/Sets.agda
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@ -70,7 +70,7 @@ module _ {ℓ : Level} where
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

11
src/Cat/Category/Product.agda
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@ -10,14 +10,15 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
open Category ℂ open Category ℂ
record RawProduct (A B : Object) : Set (ℓa ⊔ ℓb) where module _ (A B : Object) where
record RawProduct : Set (ℓa ⊔ ℓb) where
no-eta-equality no-eta-equality
field field
obj : Object obj : Object
proj₁ : ℂ [ obj , A ] proj₁ : ℂ [ obj , A ]
proj₂ : ℂ [ obj , B ] proj₂ : ℂ [ obj , B ]
record IsProduct {A B : Object} (raw : RawProduct A B) : 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} (x₁ : ℂ [ X , A ]) (x₂ : ℂ [ X , B ])
@ -28,10 +29,10 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) 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 (A B : Object) : Set (ℓa ⊔ ℓb) where record Product : Set (ℓa ⊔ ℓb) where
field field
raw : RawProduct A B raw : RawProduct
isProduct : IsProduct {A} {B} raw isProduct : IsProduct raw
open IsProduct isProduct public open IsProduct isProduct public