model category

for ∞-groupoids

# Contents

## Idea

A cartesian closed model category is a cartesian closed category that is equipped with the structure of a monoidal model category in a compatible way, which combines the axioms for a monoidal model category and an enriched model category.

## Definition

A cartesian model category (following Rezk (2010) and Simpson (2012)) is a cartesian closed category equipped with a model structure that satisfies the following additional axioms:

• (Pushout–product axiom). If $f : X \to Y$ and $f' : X' \to Y'$ are cofibrations, then the induced morphism $(Y \times X') \cup^{X \times X'} (X \times Y') \to Y \times Y'$ is a cofibration that is trivial if either $f$ or $f'$ is.

• (Unit axiom). The terminal object is cofibrant.

## References

Revised on November 11, 2013 02:18:40 by Urs Schreiber (89.204.135.29)