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.