Rodelo, DianaVan der Linden, Tim2017-04-072017-04-072016-010001-8708AUT: DRO01261;http://hdl.handle.net/10400.1/9663We 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 semiabelian 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. (C) 2015 Elsevier Inc. All rights reserved.engjournal article10.1016/j.aim.2015.09.023