*-autonomous category

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In mathematics, a *-autonomous category C is a symmetric monoidal closed category equipped with a dualizing object [\bot].

More explicitly, in every symmetric monoidal closed category C, for every objects A and [\bot], there exists a morphism

[\partial_:A\to(A\Rightarrow\bot)\Rightarrow\bot]

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

[\mathrm_\circ\gamma_ : (A\Rightarrow\bot)\otimes A\to\bot]

An object [\bot] of the category C is called dualizing when the associated morphism [\partial_] is an isomorphism for every object A of the category C.

References

Barr, Michael (1979) "*-autonomous Categories", Lecture Notes in Mathematics 752, Springer-Verlag.
Barr, Michael (1995) "Non-symmetric *-autonomous Categories", Theoretical Computer Science 139, 115–130.

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