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SUMMARY:On morphisms between diagrams\, and strictification of (∞\,n)-ca
 tegories - Amar Hadzihasanovic - Taltech
DTSTART:20250422T130000Z
DTEND:20250422T140000Z
UID:TALK230011@talks.cam.ac.uk
CONTACT:Thibaut Benjamin
DESCRIPTION:Regular directed complexes are an order-theoretic model of (sh
 apes of) higher-categorical diagrams. There are two natural notions of mor
 phism between regular directed complexes: they are called "maps" and "coma
 ps" and are dual to each other. Roughly\, a map can only collapse or rigid
 ly identify cells\, while a comap can only merge cells together.\nA subcla
 ss 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 c
 artesian maps against comaps\, which I strongly believe to be true. This c
 onjecture implies a (semi-)strictification theorem for (∞\,n)-categories
  in the same explicit\, combinatorial style as Mac Lane's celebrated stric
 tification theorem for bicategories.\nThis talk is based on joint work wit
 h Clémence Chanavat\, both past and in progress.
LOCATION:SS03\, Computer Laboratory
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