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feat: the opposite of a braided category is braided (#10095)
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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/- | ||
Copyright (c) 2024 Lean FRO LLC. All rights reserved. | ||
Released under Apache 2.0 license as described in the file LICENSE. | ||
Authors: Scott Morrison | ||
-/ | ||
import Mathlib.CategoryTheory.Monoidal.Braided.Basic | ||
import Mathlib.CategoryTheory.Monoidal.Opposite | ||
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/-! | ||
# If `C` is braided, so is `Cᵒᵖ`. | ||
Todo: we should also do `Cᵐᵒᵖ`. | ||
-/ | ||
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open CategoryTheory MonoidalCategory BraidedCategory Opposite | ||
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variable {C : Type*} [Category C] [MonoidalCategory C] [BraidedCategory C] | ||
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instance : BraidedCategory Cᵒᵖ where | ||
braiding X Y := (β_ (unop Y) (unop X)).op |
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