You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Naso (Feb 06 2022 at 16:28):Is there a categorical way to describe the maximal nondegenerate simplices (facets?) of a simplicial set?
John Baez (Feb 06 2022 at 19:52):Those that are only faces of degenerate simplices. But I guess that's too obvious, so we want to say it another way.
Naso (Feb 07 2022 at 02:03):John Baez said:
Those that are only faces of degenerate simplices. But I guess that's too obvious, so we want to say it another way.
Right, I was wondering if we could write the (graded) set of facets as a limit/colimit, for example?
Naso (Feb 07 2022 at 12:33):or could they be described in a lattice theoretic way or in the internal logic of the topos of simplicial sets, as special subobjects of a simplicial set (thinking of a facet as the subobject generated by that facet)?
Zhen Lin Low (Feb 07 2022 at 12:40):I am inclined to not believe a nice description exists. The degenerate/nondegenerate dichotomy depends, of course, on classical logic. But things that have a nice description usually work well in constructive logic.
Reid Barton (Feb 07 2022 at 12:56):The facets aren't functorial in maps of simplicial sets, so that rules out certain types of descriptions.