On morphisms between diagrams, and strictification of (∞,n)-categories

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• Amar Hadzihasanovic - Taltech
• Tuesday 22 April 2025, 14:00-15:00
• SS03, Computer Laboratory.

If you have a question about this talk, please contact Thibaut Benjamin.

Regular directed complexes are an order-theoretic model of (shapes of) higher-categorical diagrams. There are two natural notions of morphism between regular directed complexes: they are called “maps” and “comaps” and are dual to each other. Roughly, a map can only collapse or rigidly identify cells, while a comap can only merge cells together. A subclass of maps—called cartesian maps—-serves as a foundation for a model of (∞,n)-categories with exceptionally nice properties. In this talk, I will present a conjecture on the existence of a certain factorisation of cartesian maps against comaps, which I strongly believe to be true. This conjecture implies a (semi)strictification theorem for (∞,n)-categories in the same explicit, combinatorial style as Mac Lane’s celebrated strictification theorem for bicategories. This talk is based on joint work with Clémence Chanavat, both past and in progress.

This talk is part of the Logic and Semantics Seminar (Computer Laboratory) series.

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