The third cohomology group classifies double central extensions

Diana Rodelo and Tim Van der Linden

We characterise the double central extensions in a semi-abelian category in terms of commutator conditions. We prove that the third cohomology group H^3(Z,A) of an object Z with coefficients in an abelian object A classifies the double central extensions of Z by A.

Keywords: cohomology, categorical Galois theory, semi-abelian category, higher central extension, Baer sum

2000 MSC: 18G50, 18G60, 20J, 55N

Theory and Applications of Categories, Vol. 23, 2010, No. 8, pp 150-169.

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