Definition
Let C be a symmetric monoidal closed category. For any object A and, there exists a morphism
defined as the image by the bijection defining the monoidal closure, of the morphism
An object of the category C is called dualizing when the associated morphism is an isomorphism for every object A of the category C.
Equivalently, a *-autonomous category is a symmetric monoidal category C together with a functor such that for every object A there is a natural isomorphism, and for every three objects A, B and C there is a natural bijection
- .
The dualizing object of C is then defined by .
Read more about this topic: *-autonomous Category
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