nLab simplicial object in Cat

Context

Higher category theory

higher category theory

Contents

Definition

A simplicial object in $\mathrm{Cat}$ is a particular case of simplicial object, of course, with the $C$ there being $\mathrm{Cat}$. It therefore has a simplicial set of objects and a simplicial set of morphisms. This is equivalent to giving an internal category in simplicial sets.

Remark A simplicial object in $Cat$ is sometimes called a simplicial category, but that has other meanings.

References

One of the few references that discusses a model category structure on ${\mathrm{Cat}}^{\Delta }$ as opposed to just $\mathrm{sSet}\mathrm{Cat}$ is

Revised on July 21, 2013 09:03:24 by Mike Shulman (107.201.30.59)