nLab model structure on presheaves over a test 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

Idea

For $C$ a test category, the canonical structure of a category with weak equivalences on the category of presheaves over $C$ lifts to the structure of a model category. All of these are models for the standard homotopy theory (the homotopy category of ∞Grpd).

References

The model structure is due to

Further developments are in

• Rick Jardine, Categorical homotopy theory, Homot. Homol. Appl. 8 (1), 2006, pp.71–144, (HHA, pdf).

Last revised on October 15, 2020 at 17:00:13. See the history of this page for a list of all contributions to it.