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Stream: learning: questions

Topic: (infty,infty)-categories

Leopold Schlicht (Feb 28 2022 at 15:50):

There is a subclass of the class of all simplicial sets which provides a model for $(\infty,1)$-categories: the simplicial sets in which every inner horn has a filler ("weak Kan extension condition"). I just noticed that there is also a (larger) subclass of simplicial sets which provides a model for $(\infty,2)$-categories: Kerodon 01W9.

Can $(\infty,\infty)$-categories be defined as certain simplicial sets too? Is there any literature about that?

Mike Shulman (Feb 28 2022 at 15:59):

Conjecturally, yes.

Leopold Schlicht (Feb 28 2022 at 16:59):

Thanks!

Mike Shulman (Feb 28 2022 at 17:30):

Also some later work.

Leopold Schlicht (Mar 01 2022 at 19:01):

Thanks!