No CrossRef data available.
Article contents
Second cohomotopy and nonabelian cohomology
Published online by Cambridge University Press: 17 January 2014
Abstract
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.
- Type
- Research Article
- Information
- Copyright
- Copyright © ISOPP 2014
References
1.Baues, H.-J. and Wirsching, G.. Cohomology of small categories, J. Pure Appl. Algebra 38(2–3) (1985), 187–211.Google Scholar
2.Bousfield, A. K. and Kan., D. M.Homotopy limits, completions and localizations. Lecture Notes in Math. 304, Springer, 1972.Google Scholar
3.Duflot, J. and Marek, C. T.. A filtration in Algebraic K-theory. J. Pure Appl. Algebra 151 (2000), 135–162.Google Scholar
4.Grothendieck, A.. A general theory of fibre spcaes with structure sheaf, Univ. Kansas, Report 4, 1955.Google Scholar
6.May, P. J.. Simplicial objects in algebraic topology. Van Nostrand Mathematical Studies 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London 1967 vi+161 pp.Google Scholar
7.Nuss, P. and Wambst, M.. Non-abelian Hopf cohomology. II. The general case. J. Algebra 319(11) (2008), 4621–4645.CrossRefGoogle Scholar
8.Serre, J.-P.. Cohomologie galoisienne. Fifth edition. Lecture Notes Math. 5, Springer, 1994. x+184 pp.Google Scholar