Exact couples in a Raïkov semi-abelian category
Kopylov, Yaroslav
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 45 (2004), p. 162-178 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2004-01-01
@article{CTGDC_2004__45_3_162_0,
     author = {Kopylov, Yaroslav},
     title = {Exact couples in a Ra\"\i kov semi-abelian category},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     volume = {45},
     year = {2004},
     pages = {162-178},
     mrnumber = {2090333},
     zbl = {1059.18006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CTGDC_2004__45_3_162_0}
}

Kopylov, Yaroslav. Exact couples in a Raïkov semi-abelian category. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Tome 45 (2004) pp. 162-178. http://gdmltest.u-ga.fr/item/CTGDC_2004__45_3_162_0/

[1] C. Bănică and N. Popescu, Sur les catégories préabéliennes, Rev. Roumaine Math. Pures Appl. 10 (1965), 621-633. | MR 194488

[2] A. Bouarich, Suites exactes en cohomologie bornée réelle des groupes discrets, C. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 11, 1355-1359. | MR 1338286 | Zbl 0833.57023

[3] M. Burger and N. Monod, Continuous bounded cohomology and applications to rigidity theory, Geom. Funct. Anal. 12 (2002), no. 2, 219-280. | MR 1911660 | Zbl 1006.22010

[4] I. Bucur and A. Deleanu, Introduction to the theory of categories and functors, Pure and Applied Mathematics, XIX, Interscience Publication John Wiley & Sons, Ltd., London-New York-Sydney, 1968. | MR 236236 | Zbl 0197.29205

[5] B. Eckmann and P.J. Hilton, Exact couples in an abelian category, J. Algebra 3 (1966), 38-87. | MR 191937 | Zbl 0178.34306

[6] B. Eckmann and P.J. Hilton, Commuting limits with colimits, J. Algebra 11 (1969), 116-144. | MR 233865 | Zbl 0164.01301

[7] S. Eilenberg and J.C. Moore, Limits and spectral sequences, Topology 1 (1962), 1-23. | MR 148723 | Zbl 0104.39603

[8] P. Freyd, Abelian categories. An introduction to the theory of functors, Harper's Series in Modern Mathematics Harper & Row, Publishers, New York, 1964. | MR 166240 | Zbl 0121.02103

[9] N.V. Glotko and V.I. Kuz'Minov, On the cohomology sequence in a semiabelian category, Sibirsk. Mat. Zh. 43 (2002), no. 1, 41-50; English translation in: Siberian Math. J. 43 (2002), no. 1, 28-35. | MR 1888116 | Zbl 1009.18011

[10] G. Janelidze, L. Márki, and W. Tholen, Semi-abelian categories, Category theory 1999 (Coimbra), J. Pure Appl. Algebra 168 (2002), no. 2-3, 367-386. | MR 1887164 | Zbl 0993.18008

[11] Ya. A. Kopylov and V.I. Kuz'Minov, On the Ker-Coker sequence in a semi-abelian category, Sibirsk. Mat. Zh. 41 (2000), no. 3, 615-624; English translation in: Siberian Math. J. 41 (2000), no. 3, 509-517. | MR 1778676 | Zbl 0952.18003

[12] Ya. A. Kopylov and V.I. Kuz'Minov, Exactness of the cohomology sequence corresponding to a short exact sequence of complexes in a semiabelian category, Sib. Adv. Math. 13 (2003), no. 3. | MR 2028407 | Zbl 1046.18010

[13] V.I. Kuz'Minov and A. Yu. Cherevikin, Semiabelian categories, Sibirsk. Mat. Zh. 13 (1972), no. 6, 1284-1294; English translation in: Siberian Math. J. 13 (1972), no 6, 895-902. | MR 332926 | Zbl 0264.18005

[14] W.S. Massey, Exact couples in algebraic topology. I, II, Ann. of Math. (2) 56, (1952), 363-396. | MR 52770 | Zbl 0049.24002

[15] N. Monod, Continuous bounded cohomology of locally compact groups, Lecture Notes in Mathematics, 1758, Springer-Verlag, Berlin, 2001. | MR 1840942 | Zbl 0967.22006

[16] G.A. Noskov, The Hochschild-Serre spectral sequence for bounded cohomology, Proceedings of the International Conference on Algebra, Part 1 (Novosibirsk, 1989), 613-629, Contemp. Math., 131, Part 1, Amer. Math. Soc., Providence, RI, 1992. | MR 1175809 | Zbl 0773.20020

[17] N. Popescu and L. Popescu, Theory of categories, Martinus Nijhoff Publishers, The Hague; Sijthoff & Noordhoff International Publishers, Alphen aan den Rijn, 1979. | MR 538276 | Zbl 0496.18001

[18] F. Prosmans, Derived projective limits of topological abelian groups, J. Funct. Anal. 162 (1999), no. 1, 135-177. | MR 1674550 | Zbl 0916.22001

[19] F. Prosmans, Derived limits in quasi-abelian categories, Bull. Soc. Roy. Sci. Liège 68 (1999), no. 5-6, 335-401. | MR 1743618 | Zbl 0959.18006

[20] F. Prosmans, Derived categories for functional analysis, Publ. Res. Inst. Math. Sci. 36 (2000), no. 1, 19-83. | MR 1749013 | Zbl 0973.46069

[21] D.A. Raĭkov, Semiabelian categories, Dokl. Akad. Nauk SSSR 188 (1969), 1006-1009; English translation in Soviet Math. Dokl. 1969. V. 10. P. 1242-1245. | MR 255639 | Zbl 0204.33501

[22] W. Rump, *-modules, tilting, and almost abelian categories, Comm. Algebra 29 (2001), no. 8, 3293-3325; Erratum (Misprints generated via electronic editing): Comm. Algebra 30 (2002), 3567-3568. | MR 1849488 | Zbl 01656317

[23] W. Rump, Almost abelian categories, Cahiers Topologie Géom. Différentielle Catég. 42 (2001), no. 3, 163-225. | Numdam | MR 1856638 | Zbl 1004.18009

[24] J.-P. Schneiders, Quasi-abelian categories and sheaves, Mém. Soc. Math. Fr. (N.S.) (1999), no. 76. | Numdam | MR 1779315 | Zbl 0926.18004

[25] R. Succi Cruciani, Sulle categorie quasi abeliane, Rev. Roumaine Math. Pures Appl. 18 (1973), 105-119. | MR 382394 | Zbl 0278.18006

[26] J. H. C. Whitehead, The G-dual of a semi-exact couple, Proc. London Math. Soc. 3 (1953), 385-416. | MR 60826 | Zbl 0052.39801