nLab
simplicial object in Cat

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Definition

A simplicial object in CatCat is a particular case of simplicial object, of course, with the CC there being CatCat. 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\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 ΔCat^\Delta as opposed to just sSetCatsSet Cat is

A model category sturcture on Cat(sSet)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)