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agdaproofs/Categories/Dual/Definition.agda
2020-01-05 15:06:35 +00:00

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Agda

{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Categories.Definition
module Categories.Dual.Definition where
dual : {a b : _} Category {a} {b} Category {a} {b}
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) }