nLab
model structure on presheaves over a test category

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Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (∞,1)-categories

Model structures

for ∞-groupoids

for ∞-groupoids

for n-groupoids

for ∞-groups

for ∞-algebras

general

specific

for stable/spectrum objects

for (∞,1)-categories

for stable (∞,1)-categories

for (∞,1)-operads

for (n,r)-categories

for (∞,1)-sheaves / ∞-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).

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)
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