Cauchy-completions and extended TFTs

Abstract: An enriched category is said to be Cauchy-complete if it admits all absolute colimits — those weighted colimits that commute with every enriched functor. For instance, an ordinary (Set-enriched) category is Cauchy-complete precisely when it is idempotent complete, while an Ab-enriched category is so when it is both idempotent complete and additive.

I will extend this notion to enriched (∞,n)-categories and explain how, via the cobordism hypothesis, it yields a flexible and general formalism for constructing and classifying framed fully extended topological field theories. In particular, it clarifies the role of higher idempotents, also known as condensations in the sense of Gaiotto and Johnson-Freyd. Joint work in progress with David Reutter.

Mathematics

Audience: researchers in the topic

European Quantum Algebra Lectures (EQuAL)

Series comments: EQuAL is an online seminar series on quantum algebra and related topics such as topological and conformal field theory, operator algebra, representation theory, quantum topology, etc. sites.google.com/view/equalseminar/home