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A relative theory of universal central extensions
Casas, José Manuel; Linden, Tim Van derBasing ourselves on Janelidze and Kelly’s general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new results in one conceptual framework. The theory we develop is relative with respect to a chosen Birkhoff subcategory of the category considered: for instance, we consider groups vs. abelian groups, Lie algebras vs....
A note on double central extensions in exact Mal'tsev categories
Everaert, Tomas; Linden, Tim Van derThe characterisation of double central extensions in terms of commutators due to Janelidze (in the case of groups), Gran and Rossi (in the case of Mal'tsev varieties) and Rodelo and Van der Linden (in the case of semi-abelian categories) is shown to be still valid in the context of exact Mal'tsev categories. ; CMUC/FCT; FWO
The third cohomology group classifies double central extensions
Rodelo, Diana; Linden, Tim Van derWe characterise the double central extensions in a semi-abelian category in terms of commutator conditions. We prove that the third cohomology group H3(Z;A) of an object Z with coe cients in an abelian object A classi es the double central extensions of Z by A. ; FCT/Centro de Matemática da Universidade de Coimbra; Vrije Universiteit Brussel
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