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.
http://www.tac.mta.ca/tac/volumes/23/8/23-08.dvi
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http://www.tac.mta.ca/tac/volumes/23/8/23-08.pdf
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