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2001 Stacks and the homotopy theory of simplicial sheaves
J. F. Jardine
Homology Homotopy Appl. 3(2): 361-384 (2001).

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.

Citation

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J. F. Jardine. "Stacks and the homotopy theory of simplicial sheaves." Homology Homotopy Appl. 3 (2) 361 - 384, 2001.

Information

Published: 2001
First available in Project Euclid: 13 February 2006

zbMATH: 0995.18006
MathSciNet: MR1856032

Subjects:
Primary: 18G50
Secondary: 14A20, 18F20, 18G30

Rights: Copyright © 2001 International Press of Boston

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Vol.3 • No. 2 • 2001
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