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Use long name for product object

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This commit is contained in:
Frederik Hanghøj Iversen 2018-03-08 10:45:15 +01:00
parent 486238e114
commit 63b5f5c68d
3 changed files with 12 additions and 11 deletions
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6
src/Cat/Categories/Cat.agda
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@ -152,9 +152,9 @@ module _ {ℓ ℓ' : Level} (unprovable : IsCategory (RawCat ℓ ℓ')) where
module P = CatProduct ℂ 𝔻 module P = CatProduct ℂ 𝔻
rawProduct : RawProduct Catℓ ℂ 𝔻 rawProduct : RawProduct Catℓ ℂ 𝔻
RawProduct.obj rawProduct = P.obj RawProduct.object rawProduct = P.obj
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

6
src/Cat/Categories/Sets.agda
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@ -66,9 +66,9 @@ module _ {ℓ : Level} where
proj₂ lem = refl proj₂ lem = refl
rawProduct : RawProduct 𝓢 0A 0B rawProduct : RawProduct 𝓢 0A 0B
RawProduct.obj rawProduct = 0A×0B RawProduct.object 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

11
src/Cat/Category/Product.agda
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@ -1,3 +1,4 @@
{-# OPTIONS --allow-unsolved-metas #-}
module Cat.Category.Product where module Cat.Category.Product where
open import Agda.Primitive open import Agda.Primitive
@ -14,9 +15,9 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
record RawProduct : Set (ℓa ⊔ ℓb) where record RawProduct : Set (ℓa ⊔ ℓb) where
no-eta-equality no-eta-equality
field field
obj : Object object : Object
proj₁ : ℂ [ obj , A ] proj₁ : ℂ [ object , A ]
proj₂ : ℂ [ obj , B ] proj₂ : ℂ [ object , B ]
-- FIXME Not sure this is actually a proposition - so this name is -- FIXME Not sure this is actually a proposition - so this name is
-- misleading. -- misleading.
@ -28,7 +29,7 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
-- | Arrow product -- | Arrow product
_P[_×_] : ∀ {X} → (π₁ : ℂ [ X , A ]) (π₂ : ℂ [ X , B ]) _P[_×_] : ∀ {X} → (π₁ : ℂ [ X , A ]) (π₂ : ℂ [ X , B ])
→ ℂ [ X , obj ] → ℂ [ X , object ]
_P[_×_] π₁ π₂ = P.proj₁ (isProduct π₁ π₂) _P[_×_] π₁ π₂ = P.proj₁ (isProduct π₁ π₂)
record Product : Set (ℓa ⊔ ℓb) where record Product : Set (ℓa ⊔ ℓb) where
@ -43,7 +44,7 @@ module _ {ℓa ℓb : Level} (ℂ : Category ℓa ℓb) where
product : ∀ (A B : Object) → Product A B product : ∀ (A B : Object) → Product A B
_×_ : Object → Object → Object _×_ : Object → Object → Object
A × B = Product.obj (product A B) A × B = Product.object (product A B)
-- | Parallel product of arrows -- | Parallel product of arrows
-- --