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Stream: theory: category theory

Topic: ✔ Dualizable objects in Prof

Daniel Teixeira (Nov 27 2023 at 13:14):

Mike Shulman said:

The dual of a category $C$ in $\mathrm{Prof}$ is its opposite $C^{\mathrm{op}}$, and the unit and counit are both its hom-functor.

thanks Mike, I worked the triangle identities from here and I got to a formula that should be the identity in Prof up to my lack of knowledge about coends

Notification Bot (Nov 27 2023 at 13:14):

Daniel Teixeira has marked this topic as resolved.

Nathanael Arkor (Nov 27 2023 at 15:24):

It may be worth pointing out that dual objects in Prof are only determined up to [[Morita equivalence]], not up to [[equivalence of categories]]. So the [[Cauchy completion]] of $C^{\text{op}}$ is also the dual of $C$ in Prof.