Higher central extensions and cohomology

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.

arXiv comment58 pages

References in corpus (12)

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• A note on the "Smith is Huq" condition
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Cited by in corpus (10)

• Two characterisations of groups amongst monoids
• The Yoneda isomorphism commutes with homology
• Non-associative algebras
• An introduction to regular categories
• On the "three subobjects lemma" and its higher-order generalisations
• Non-additive derived functors via chain resolutions
• Higher extensions in exact Mal'tsev categories: distributivity of congruences and the $3^n$-Lemma
• A symmetric approach to higher coverings in categorical Galois theory
• Categorical-algebraic aspects of Heyting semilattices
• Twisted Commutators and Internal Crossed Modules