nLab
model structure on presheaves over a test category
Context
Model category theory
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of $(\infty,1)$categories
Model structures
for $\infty$groupoids
for $n$groupoids
for $\infty$groups
for $\infty$algebras
general
specific




and on /
related by the

: , ,

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).
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)
Last revised on October 11, 2012 at 16:48:29.
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