COSIMPLICIAL SPACES AND COCYCLES
2014 ◽
Vol 15
(3)
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pp. 445-470
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.
1964 ◽
Vol 113
(1)
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pp. 40-40
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1988 ◽
Vol 103
(3)
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pp. 427-449
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1958 ◽
Vol 7
(2)
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pp. 237-264
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2008 ◽
Vol 1
(3)
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pp. 431-472
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2006 ◽
pp. 23-33
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