On the second cohomology categorical group and a Hochschild-Serre 2-exact sequence

A.R. Garzon and E.M. Vitale

We introduce the second cohomology categorical group of a categorical group G with coefficients in a symmetric G-categorical group and we show that it classifies extensions of G with symmetric kernel and a functorial section. Moreover, from an essentially surjective homomorphism of categorical groups we get 2-exact sequences a la Hochschild-Serre connecting the categorical groups of derivations and the first and the second cohomology categorical groups.

Keywords: (symmetric) categorical group, 2-exactness, cohomology categorical group, extension

2010 MSC: 18D10, 18B40, 18D35, 18G50, 20J06

Theory and Applications of Categories, Vol. 30, 2015, No. 27, pp 933-984.

Published 2015-07-07.


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