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https://github.com/Smaug123/agdaproofs
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15 lines
781 B
Agda
15 lines
781 B
Agda
{-# OPTIONS --warning=error --safe --without-K #-}
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open import LogicalFormulae
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import Categories.Definition
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module Categories.Functor.Definition where
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record Functor {a b c d : _} (C : Category {a} {b}) (D : Category {c} {d}) : Set (a ⊔ b ⊔ c ⊔ d) where
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field
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onObj : Category.objects C → Category.objects D
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onArrow : {S T : Category.objects C} → Category.arrows C S T → Category.arrows D (onObj S) (onObj T)
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mapId : {T : Category.objects C} → onArrow (Category.id C T) ≡ Category.id D (onObj T)
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mapCompose : {X Y Z : Category.objects C} → (f : Category.arrows C X Y) (g : Category.arrows C Y Z) → onArrow (Category._∘_ C g f) ≡ Category._∘_ D (onArrow g) (onArrow f)
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