Category Theory
Zulip Server
Archive

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.

Stream: learning: questions

Topic: 2-category of simplicial sets

Leopold Schlicht (Oct 26 2021 at 16:48):

Is there a natural 2-category of simplicial sets?

There is a fully faithful functor from the category of all small categories to the category of simplicial sets. The motivation for the question is that it might be more natural to consider the "collection" of all small categories as a 2-category.

Daniel Teixeira (Oct 26 2021 at 19:26):

I'm not sure what you're asking for. The most natural "2-category of simplicial sets" is obtained by enriching $\mathsf{sSet}$ over itself and considering its image through the functor $h_*:\mathsf{Cat_{sSet}\to Cat_{Cat}}$ induced by the right adjoint of the nerve. This eventually leads to [[infinity-cosmos]] and all that.

it might be more natural to consider the "collection" of all small categories as a 2-category.

in what context are you talking about?

Leopold Schlicht (Oct 28 2021 at 17:09):

Thanks! I don't really know what you mean by "context".