nLab
Thomason model category

Contents

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

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

Model structures

for \infty-groupoids

for ∞-groupoids

for equivariant \infty-groupoids

for rational \infty-groupoids

for rational equivariant \infty-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

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

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

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

for (,1)(\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 04:17:18. See the history of this page for a list of all contributions to it.