# nLab model (∞,1)-category

Contents

### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

for ∞-groupoids

# Contents

## Idea

The notion of model $(\infty,1)$-category (or model $\infty$-category, for short) is the $(\infty,1)$-categorification of that of model category.

Where the classical model structure on simplicial sets is an archetypical example of a model category, so simplicial $\infty$-groupoids (“simplicial spaces”, bisimplicial sets) form an archetypical example of a model $\infty$-category. In this example, a fundamental application of the theory says, for instance, that geometric realization preserves homotopy pullbacks of homotopy Kan fibrations (see there).

## References

Created on December 28, 2021 at 14:09:32. See the history of this page for a list of all contributions to it.