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twisting by a cocycle

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Second cohomotopy and nonabelian cohomology
Mariam Pirashvili
Journal:

Journal of K-Theory / Volume 13 / Issue 3 / June 2014

Published online by Cambridge University Press:

17 January 2014, pp. 397-445

Print publication:

June 2014
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The main difficulty in the theory of non-abelian cohomology is that for cosimplicial groups only zero-th and first dimensional cohomotopy are known. In this article we introduce a new class of cosimplicial groups, called centralised cosimplicial groups, for which we are able to define a second cohomotopy, with all expected properties. The main examples of such cosimplicial groups come from 2-categories.