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Stream: theory: category theory

Topic: Reference for *-autonomous categories

JS PL (he/him) (Feb 04 2022 at 14:59):

I'm looking for a reference (with a proof) for the result that states that a *-autonomous category is compact closed if and only if the unit is the dualizing object and the canonical map $A^* \otimes B^* \to (A \otimes B)^*$ is a natural isomorphism.

JS PL (he/him) (Feb 04 2022 at 15:00):

It's a well-known result but most of the standard references for *-autonomous categories simply state it in passing in the introduction. And it would be nice to have an actual statement that we can cite.