canonical model structure on groupoids
Model category theory
Producing new model structures
Presentation of -categories
for stable/spectrum objects
for stable -categories
for -sheaves / -stacks
The natural model category structure on the 1-category of groupoids and functors is a presentation of the (2,1)-category of groupoids, functors and natural isomorphisms.
This is one flavor of the various natural model structures on categories and higher categories.
Equipped with this structure is a model category which is
This is originally due to (Anderson) and (Bousfield). A detailed discussion is in section 6 of (Strickland). In the context of the model structure for (2,1)-sheaves it appears as (Hollander, theorem 2.1).
See natural model structure for more.
be the pair of adjoint functors, where is the nerve of groupoids with values in sSet.
With the natural model structure on and the standard model structure on simplicial sets this is a Quillen adjunction
and is the transferred model structure obtained from under this adjunction.
This model category structure appears originally in
- D.W. Anderson, Fibrations and Geometric Realizations , Bull. Am. Math Soc. 84, 765-786, (1978), 765-786.
- A. K. Bousfield, Homotopy Spectral Sequences and Obstructions , Israel Journal of Math., Vol.66, Nos.1-3, (1989), 54-105.
A detailed description is in section 6 of
- Neil Strickland -local duality for finite groups and groupoids , Topology 39, (2000).
The model structure on functors with values in (a model structure for (2,1)-sheaves) is discussed in
Revised on November 23, 2012 19:28:00
by Urs Schreiber