Geodesic
On the second cohomology categorical group and a Hochschild-Serre 2-exact sequence
Theory and applications of categories, Tome 30 (2015), pp. 933-984.

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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.
Publié le :
Classification : 18D10, 18B40, 18D35, 18G50, 20J06
Keywords: (symmetric) categorical group, 2-exactness, cohomology categorical group, extension 
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     author = {A.R. Garzon and E.M. Vitale},
     title = {On the second cohomology categorical group and a {Hochschild-Serre} 2-exact sequence},
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     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2015_30_a26/}
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A.R. Garzon; E.M. Vitale. On the second cohomology categorical group and a Hochschild-Serre 2-exact sequence. Theory and applications of categories, Tome 30 (2015), pp. 933-984. http://geodesic.mathdoc.fr/item/TAC_2015_30_a26/