nLab
model structure on presheaves over a test category

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 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

Idea

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

Examples

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)
Revised on October 11, 2012 16:48:29 by Anonymous Coward (93.129.84.175)