# nLab Thomason model category

Contents

### Context

#### Model category theory

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of $(\infty,1)$-categories

Model structures

for $\infty$-groupoids

for ∞-groupoids

for equivariant $\infty$-groupoids

for rational $\infty$-groupoids

for rational equivariant $\infty$-groupoids

for $n$-groupoids

for $\infty$-groups

for $\infty$-algebras

general $\infty$-algebras

specific $\infty$-algebras

for stable/spectrum objects

for $(\infty,1)$-categories

for stable $(\infty,1)$-categories

for $(\infty,1)$-operads

for $(n,r)$-categories

for $(\infty,1)$-sheaves / $\infty$-stacks

# Contents

## Definition

A Thomason model category is a (Quillen) model category such that functorial factorizations exist.

## Properties

A functor category with values in a Thomason model category is automatically again a Thomason model category and hence yields a notion of global model structure on functors.

Mark Hovey later popularized this addition, including the data of functorial factorizations (and not just their existence) into his definition of a model category (he attributed this addition to Dwyer–Hirschhorn–Kan–Smith).

## References

See Weibel’s Thomason obituary for some details.

Last revised on May 7, 2020 at 08:17:18. See the history of this page for a list of all contributions to it.