Chain complexes of symmetric categorical groups

del Rio, A;Martinez-Moreno, J;Vitale, Enrico
(2005) Journal of Pure and Applied Algebra — Vol. 196, n° 2-3, p. 279-312 (2005)

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Abstract
We define the cohomology categorical groups of a complex of symmetric categorical groups, and we construct a long 2-exact sequence from an extension of complexes. As special cases, we obtain Ulbrich cohomology of Picard categories and the Hattori-Villamayor-Zelinsky sequences associated with a ring homomorphism. Applications to simplicial cohomology with coefficients in a symmetric categorical group, and to derivations of categorical groups are also discussed. (C) 2004 Elsevier B.V. All rights reserved.
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del Rio, A., Martinez-Moreno, J., & Vitale, E. (2005). Chain complexes of symmetric categorical groups. Journal of Pure and Applied Algebra, 196(2-3), 279-312. https://doi.org/10.1016/j.jpaa.2004.08.029 (Original work published 2005)