The third cohomology group classifies double central extensions

Rodelo, Diana;Van der Linden, Tim
(2010) Theory and Applications of Categories — Vol. 23, n° 8, p. 150-169 (2010)

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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.
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Rodelo, D., & Van der Linden, T. (2010). The third cohomology group classifies double central extensions. Theory and Applications of Categories, 23(8), 150-169. https://hdl.handle.net/2078.5/59972 (Original work published 2010)