nLab simplicial object in Cat

Context

Higher category theory

higher category theory

Contents

Definition

A simplicial object in $Cat$ is a particular case of simplicial object, of course, with the $C$ there being $Cat$. 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 $Cat^\Delta$ as opposed to just $sSet Cat$ is

A model category sturcture on $Cat(sSet)$ presenting (infinity,1)-categories is in

• Geoffroy Horel, A model structure on internal categories (arXiv:1403.6873).

Revised on March 29, 2014 03:03:10 by Urs Schreiber (185.37.147.12)