A Homotopy Theory for Stacks
Sharon Hollander
Department of Mathematics, MIT
Cambridge, MA 02139
sharon@math.mit.edu
AMS Classification: Primary 14A20 ; Secondary 18G55, 55U10
We give a homotopy theoretic characterization of stacks on a site $\cC$
as the {\it homotopy sheaves} of groupoids on $\cC$.
We use this characterization to construct a model category
in which stacks are the fibrant objects.
We compare different definitions of stacks and show
that they lead to Quillen equivalent model categories.
In addition, we show that these model structures
are Quillen equivalent to the $S^2$-nullification
of Jardine's model structure on sheaves of simplicial sets on $\cC$.