Low-dimensional cohomology for categorical groups

Garzón, B. A. R.; del Rio, A.

Garzón, B. A. R. ; del Rio, A.

Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 4, pp. 247-280.

MR Zbl

@article{CTGDC_2003__44_4_247_0,
     author = {Garz\'on, B. A. R. and del Rio, A.},
     title = {Low-dimensional cohomology for categorical groups},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     pages = {247--280},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {44},
     number = {4},
     year = {2003},
     mrnumber = {2030048},
     zbl = {1042.18006},
     language = {en},
     url = {http://www.numdam.org/item/CTGDC_2003__44_4_247_0/}
}

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Garzón, B. A. R.; del Rio, A. Low-dimensional cohomology for categorical groups. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 44 (2003) no. 4, pp. 247-280. http://www.numdam.org/item/CTGDC_2003__44_4_247_0/

Bibliographie
Cité par

[1] Borceux, F. Handbook of categorical algebra 1,2. Cambridge University Press, 1994. | MR

[2] Breen, L. Théorie de Schreier supérieure. Ann. Scient. Éc. Norm. Sup. 1992, ,4e série, 25, 465-514. | Numdam | MR | Zbl

[3] Brown, R.; Gilbert, N.D. Algebraic models of 3-types and automorphisms structure for crossed modules. Proc. London Math. Soc. 1989, 59(3), 51-73. | MR | Zbl

[4] Bullejos, M.; Cegarra, A.M. A 3-dimensional non-abelian cohomology with applications to homotopy classification of continuous maps. Canadian Journal of Mathematics 1991, 43 (2), 265-296. | MR | Zbl

[5] Carrasco, P.; Cegarra, A.M. Schreier theory for central extensions of categorical groups. Communications in Algebra 1996, 24 (13), 4059-4112. | MR | Zbl

[6] Carrasco, P.; Garzón, A.R.; Miranda, J.G. Schreier theory for singular extensions of categorical groups and homotopy classification. Communications in Algebra 2000, 28 (5), 2585-2613. | MR | Zbl

[7] Carrasco, P.; Garzón, A.R. Obstruction theory for extensions of categorical groups. Applied Categoriques Structures (to appear). | MR | Zbl

[8] Cegarra, A.M.; Fernández, L. Cohomology of cofibred categorical groups. J. Pure Appl. Algebra 1999, 143, 107-154. | MR | Zbl

[9] Conduché, D. Modules croisés generalisés de longeur 2. J. Pure Appl. Algebra 1984, 34, 155-178. | MR | Zbl

[10] Dedecker, P. Cohomologie non-abélienne. Séminaire de l'Institut Mathématique Lille, 1965. | Zbl

[11] Garzón, A.R.; Miranda, J.G. Homotopy theory for (braided) cat-groups. Cahiers Top. et Geom. Diff. Cat. 1997, XXXVIII-2, 99-139. | EuDML | Numdam | MR | Zbl

[12] Garzón, A.R.; Inassaridze, H. Semidirect products of categorical groups. Obstruction theory. Homology, Homotopy and its applications 2001, 3 (6), 111-138. | EuDML | MR | Zbl

[13] Garzón A.R.;Del Rio, A. The Whitehead categorical group of derivations. Georgian Math. J. 2002, 9 (4), 709-721. | EuDML | MR | Zbl

[14] Garzón, A.R.; Inassaridze, H.; Del Rio, A. Derivations of categorical groups. Preprint 2002. | MR | Zbl

[15] Gilbert, N.D. Derivations, Automorphisms and Crossed Modules. Communications in Algebra 1990, 18 (8), 2703-2734. | MR | Zbl

[16] Hattory, A. On the groups Hn(S, G) and the Brauer group of commutative rings. Sci. Papers College Gen. Ed. Univ. Tokyo 1978 28, 1-20. | MR | Zbl

[17] Hilton P.J.; Stammbach U. A course in Homological Algebra. Springer Verlag 1970. | MR | Zbl

[18] Joyal, A.; Street, R. Braided tensor categories. Advances in Math. 1991, 82(1), 20-78. | MR | Zbl

[19] Kasangian, S.; Vitale, E.M. Factorization systems for symmetric cat-groups. Theory and Applications of Categories 2000, 7, (5), 47-70. | EuDML | Zbl

[20] Kelly, G.M. On Mac Lane's conditions for coherence of natural associativities, commutativities, etc. J. of Algebra 1964, 1, 397-402. | MR | Zbl

[21] Mac Lane, S. Natural associativity and commutativity. Rice University Studies 1963, 49, 28-46. | MR | Zbl

[22] Mac Lane, S. Homology. Springer, 1963. | Zbl

[23] Mac Lane, S. Categories for the working mathematician, Second edition. Springer-Verlag, 1997. | MR | Zbl

[24] Norrie, K.J. Actions and automorphisms of crossed modules. Bull. Soc. Math. France 1990, 118, 129-146. | EuDML | Numdam | MR | Zbl

[25] Rousseau, A. Extensions de Gr-catégories. Université Paris 13, Thése de doctorat, 2000.

[26] Saavedra, N. Catégories tannakiennes. Springer Lecture Notes in Math. 1972, 265. | MR | Zbl

[27] Sinh, H.X. Gr-catégories. Université Paris VII, Thèse de doctorat, 1975.

[28] Ulbrich, K.H. Group Cohomology for Picard Categories. J. of Algebra 1984, 91, 464-498. | MR | Zbl

[29] Vitale, E.M. A Picard-Brauer exact sequence of categorical groups. J. Pure Appl. Algebra 2002, 175, 383-408. | MR | Zbl