mirror of
https://github.com/Smaug123/agdaproofs
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40 lines
1.4 KiB
Agda
40 lines
1.4 KiB
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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open import Categories.Definition
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open import Groups.Definition
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module Categories.Examples where
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SET : {a : _} → Category {lsuc a} {a}
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Category.objects (SET {a}) = Set a
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Category.arrows (SET {a}) = λ a b → (a → b)
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Category.id (SET {a}) = λ x → λ y → y
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Category._∘_ (SET {a}) = λ f g → λ x → f (g x)
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Category.rightId (SET {a}) = λ f → refl
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Category.leftId (SET {a}) = λ f → refl
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Category.compositionAssociative (SET {a}) = λ f g h → refl
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GROUP : {a b : _} → Category {lsuc a ⊔ b} {a ⊔ b}
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Category.objects (GROUP {a}) = Group {!!} {!!}
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Category.arrows (GROUP {a}) = {!!}
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Category.id (GROUP {a}) = {!!}
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Category._∘_ (GROUP {a}) = {!!}
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Category.rightId (GROUP {a}) = {!!}
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Category.leftId (GROUP {a}) = {!!}
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Category.compositionAssociative (GROUP {a}) = {!!}
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DISCRETE : {a : _} (X : Set a) → Category {a} {a}
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Category.objects (DISCRETE X) = X
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Category.arrows (DISCRETE X) = λ a b → a ≡ b
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Category.id (DISCRETE X) = λ x → refl
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Category._∘_ (DISCRETE X) = λ y=z x=y → transitivity x=y y=z
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Category.rightId (DISCRETE X) = {!!}
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Category.leftId (DISCRETE X) = {!!}
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Category.compositionAssociative (DISCRETE X) = {!!}
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