*-autonomous category

In mathematics, a *-autonomous (read "star-autonomous") category C is a symmetric monoidal closed category equipped with a dualizing object ${\displaystyle \bot }$.

Let C be a symmetric monoidal closed category. For any object A and ${\displaystyle \bot }$, there exists a morphism

defined as the image by the bijection defining the monoidal closure, of the morphism

where ${\displaystyle \gamma }$ is the symmetry of the tensor product. An object ${\displaystyle \bot }$ of the category C is called dualizing when the associated morphism ${\displaystyle \partial _{A,\bot }}$ is an isomorphism for every object A of the category C.

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