nLab simplicial object in Cat

Contents

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 simplicial object, in to the 1-category Cat of categories and functors between them, equivalently an internal category in sSet.

This would deserve to be and sometimes is called a simplicial category, but more often the latter terminology is used to refer to simplicially enriched categories only (which may be regarded as the special case of simplicial objects in CatCat whose simplicial set of objects happens to be simplicially constant).

References

One of the few references that discusses a model category structure on Cat Δ opCat^{\Delta^{op}} as opposed to just sSetCatsSet Cat (but see at canonical model structure on Cat) is:

A model category stucture on Cat(sSet)Cat(sSet) presenting (infinity,1)-categories:

Last revised on December 13, 2023 at 18:11:26. See the history of this page for a list of all contributions to it.