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29 lines
777 B
Agda
29 lines
777 B
Agda
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{-# OPTIONS --without-K --safe #-}
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open import Categories.Category
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open import Categories.Category.Cartesian
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open import Categories.Category.BinaryProducts
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open import Categories.Category.Cocartesian
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import Categories.Morphism as M
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module Distributive.Core {o ℓ e} (𝒞 : Category o ℓ e) where
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open import Level
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open Category 𝒞
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open M 𝒞
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record Distributive : Set (levelOfTerm 𝒞) where
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field
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cartesian : Cartesian 𝒞
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cocartesian : Cocartesian 𝒞
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open Cartesian cartesian
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open BinaryProducts products
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open Cocartesian cocartesian
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distribute : ∀ {A B C} → (A × B + A × C) ⇒ (A × (B + C))
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distribute = [ id ⁂ i₁ , id ⁂ i₂ ]
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field
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iso : ∀ {A B C} → IsIso (distribute {A} {B} {C})
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