28 lines
979 B
Agda
28 lines
979 B
Agda
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open import Categories.Category.Core
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open import Algebra.Group
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open import Data.Unit.Polymorphic
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open import Relation.Binary.PropositionalEquality as ≡ using (_≡_)
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module Category.Construction.GroupAsCategory {ℓ} (G : Group ℓ) where
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open Group G
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GroupAsCategory : Category ℓ ℓ ℓ
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GroupAsCategory = record
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{ Obj = ⊤
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; _⇒_ = λ _ _ → Carrier
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; _≈_ = _≡_
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; id = ε
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; _∘_ = _∙_
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; assoc = assoc
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; sym-assoc = ≡.sym assoc
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; identityˡ = idˡ
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; identityʳ = idʳ
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; identity² = idˡ
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; equiv = record
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{ refl = ≡.refl
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; sym = ≡.sym
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; trans = ≡.trans
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}
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; ∘-resp-≈ = ∙-resp
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}
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