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COSIMPLICIAL SPACES AND COCYCLES

Part of: Algebraic geometry: Foundations Applied homological algebra and category theory Homological algebra

Published online by Cambridge University Press:  10 November 2014

J. F. Jardine
J. F. Jardine*
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada (jardine@uwo.ca)
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Abstract

Standard results from non-abelian cohomology theory specialize to a theory of torsors and stacks for cosimplicial groupoids. The space of global sections of the stack completion of a cosimplicial groupoid $G$ is weakly equivalent to the Bousfield–Kan total complex of $BG$ for all cosimplicial groupoids $G$. The $k$-invariants for the Postnikov tower of a cosimplicial space $X$ are naturally elements of stack cohomology for the stack associated to the fundamental groupoid ${\it\pi}(X)$ of $X$. Cocycle-theoretic ideas and techniques are used throughout the paper.

Keywords

cosimplicial spacesnon-abelian cohomologycocycles

MSC classification

Primary: 55U35: Abstract and axiomatic homotopy theory
Secondary: 18G50: Nonabelian homological algebra 14A20: Generalizations (algebraic spaces, stacks)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 3 , July 2016 , pp. 445 - 470
Copyright
© Cambridge University Press 2014 

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