Dagger category

In mathematics, a dagger category (also called involutive category or category with involution ) is a category equipped with a certain structure called dagger or involution. The name dagger category was coined by Selinger.

A dagger category is a category ${\displaystyle {\mathcal {C}}}$ equipped with an involutive functor ${\displaystyle \dagger \colon {\mathcal {C}}^{op}\rightarrow {\mathcal {C}}}$ that is the identity on objects, where ${\displaystyle {\mathcal {C}}^{op}}$ is the opposite category.

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