Stacks and the homotopy theory of simplicial sheaves, by J.F. Jardine

A stack is a sheaf of groupoids which satisfies the effective descent condition. This paper discusses the various constructions and properties of the stack completion functor in terms of the simplicial sheaf homotopy type of the associated classifying space. A homotopy classification result is given for torsors with coefficients in an arbitrary sheaf of groupoids, and path components of the quotient stack for a group action are identified with morphisms in the homotopy category taking values in the associated Borel construction.

J.F. Jardine <>