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10 lines
643 B
Agda
10 lines
643 B
Agda
{-# OPTIONS --warning=error --safe --without-K #-}
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open import LogicalFormulae
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open import Categories.Definition
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module Categories.Dual.Definition where
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dual : {a b : _} → Category {a} {b} → Category {a} {b}
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dual record { objects = objects ; arrows = arrows ; id = id ; _∘_ = _∘_ ; rightId = rightId ; leftId = leftId ; compositionAssociative = associative } = record { objects = objects ; arrows = λ i j → arrows j i ; id = id ; _∘_ = λ {x y z} g f → f ∘ g ; rightId = λ {x y} f → leftId f ; leftId = λ {x y} f → rightId f ; compositionAssociative = λ {x y z w} f g h → equalityCommutative (associative h g f) }
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