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arXiv · 1502.05282

Higher central extensions and cohomology

Diana Rodelo·Tim Van der Linden
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Abstract

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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Diana Rodelo, Tim Van der Linden. 2015-02-18. Higher central extensions and cohomology. https://doi.org/10.1016/j.aim.2015.09.023

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