35 lines
866 B
Agda
35 lines
866 B
Agda
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module Category.Sets where
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open import Cubical.PathPrelude
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open import Agda.Primitive
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open import Category
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-- Sets are built-in to Agda. The set of all small sets is called Set.
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Fun : {ℓ : Level} → ( T U : Set ℓ ) → Set ℓ
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Fun T U = T → U
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Sets : {ℓ : Level} → Category {lsuc ℓ} {ℓ}
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Sets {ℓ} = record
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{ Object = Set ℓ
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; Arrow = λ T U → Fun {ℓ} T U
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; 𝟙 = λ x → x
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; _⊕_ = λ g f x → g ( f x )
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; assoc = refl
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; ident = funExt (λ x → refl) , funExt (λ x → refl)
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}
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module _ {ℓ ℓ' : Level} {ℂ : Category {ℓ} {ℓ}} where
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private
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C-Obj = Object ℂ
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_+_ = Arrow ℂ
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RepFunctor : Functor ℂ Sets
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RepFunctor =
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record
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{ F = λ A → (B : C-Obj) → Hom {ℂ = ℂ} A B
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; f = λ { {c' = c'} f g → {!HomFromArrow {ℂ = } c' g!}}
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; ident = {!!}
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; distrib = {!!}
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}
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