# 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.

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 August 9, 2011 16:17:25 by Urs Schreiber (194.81.173.104)