arXiv 1502.052822015-02-18math.CT

Higher central extensions and cohomology

Diana Rodelo, Tim Van der Linden

备注：: 58 pages
发表信息：: Adv. Math. 287 (2016) 31-108
DOI：: 10.1016/j.aim.2015.09.023

英文摘要：

We establish a Galois-theoretic interpretation of cohomology in semi-abelian categories: cohomology with trivial coefficients classifies central extensions, also in arbitrarily high degrees. This allows us to obtain a duality, in a certain sense, between "internal" homology and "external" cohomology in semi-abelian categories. These results depend on a geometric viewpoint of the concept of a higher central extension, as well as the algebraic one in terms of commutators.

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