### Stacks and the homotopy theory of simplicial sheaves

J. F. Jardine
Source: Homology Homotopy Appl. Volume 3, Number 2 (2001), 361-384.

#### Abstract

Stacks are described as sheaves of groupoids $G$ satisfying an effective descent condition, or equivalently such that the classifying object $BG$ satisfies descent. The set of simplicial sheaf homotopy classes $[*,BG]$ is identified with equivalence classes of acyclic homotopy colimits fibred over $BG$, generalizing the classical relation between torsors and non-abelian cohomology. Group actions give rise to quotient stacks, which appear as parameter spaces for the separable transfer construction in special cases.

First Page:
Primary Subjects: 18G50
Secondary Subjects: 14A20, 18F20, 18G30
Full-text: Open access