mirror of
https://github.com/Smaug123/agdaproofs
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21 lines
844 B
Agda
21 lines
844 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 Numbers.Naturals.Naturals
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open import Numbers.Naturals.Order
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open import Vectors
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open import Semirings.Definition
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module Categories.Definition where
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record Category {a b : _} : Set (lsuc (a ⊔ b)) where
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field
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objects : Set a
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arrows : objects → objects → Set b
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id : (x : objects) → arrows x x
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_∘_ : {x y z : objects} → arrows y z → arrows x y → arrows x z
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rightId : {x y : objects} → (f : arrows x y) → (id y) ∘ f ≡ f
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leftId : {x y : objects} → (f : arrows x y) → f ∘ (id x) ≡ f
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compositionAssociative : {x y z w : objects} → (f : arrows z w) → (g : arrows y z) → (h : arrows x y) → (f ∘ (g ∘ h)) ≡ (f ∘ g) ∘ h
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