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Karoubi envelopes, semifunctors, and the extensional lambda calculus

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If you have a question about this talk, please contact Nathanael Arkor.

We take a dive into the world of semicategories, a place in which categories lose their sense of identity. Here, we can re-enact the story of the (nonextensional) simply-typed lambda calculus and cartesian-closed (semi)categories, so long as we are happy to abandon the eta-laws. Fortunately, not all is lost, as the Karoubi envelope construction gives us a canonical way to perform extensional completions of type theories.

This talk is part of the Logic & Semantics for Dummies series.

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