Cohomology without projectives

Dominique Bourn; Diana Rodelo

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2007)

  • Volume: 48, Issue: 2, page 104-153
  • ISSN: 1245-530X

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Bourn, Dominique, and Rodelo, Diana. "Cohomology without projectives." Cahiers de Topologie et Géométrie Différentielle Catégoriques 48.2 (2007): 104-153. <http://eudml.org/doc/91715>.

@article{Bourn2007,
author = {Bourn, Dominique, Rodelo, Diana},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {effectively regular, natural Mal'cev category; cohomology theory of almost abelian categories; long exact sequence of cohomology theory},
language = {eng},
number = {2},
pages = {104-153},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Cohomology without projectives},
url = {http://eudml.org/doc/91715},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Bourn, Dominique
AU - Rodelo, Diana
TI - Cohomology without projectives
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2007
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 48
IS - 2
SP - 104
EP - 153
LA - eng
KW - effectively regular, natural Mal'cev category; cohomology theory of almost abelian categories; long exact sequence of cohomology theory
UR - http://eudml.org/doc/91715
ER -

References

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  1. [1] M. Barr, Exact categories, Springer L.N. in Math., 236, 1971, pp 1-120. Zbl0223.18010
  2. [2] F. Borceux and D. Bourn, Mal'cev, protomodular, homological and semi-abelian categories, Kluwer, Mathematics and its application, vol. 566, 2004, 479 pp. Zbl1061.18001MR2044291
  3. [3] N. Bourbaki, Topologie Générale, Ch. III, Hermann, 1951. 
  4. [4] D. Bourn, The tower of n-groupoids and the long cohomology sequence, J. Pure Appl. Algebra, 62, 1989, 137-183. Zbl0699.18002MR1027753
  5. [5] D. Bourn, Another denormalization theorem for abelian chain complexes, J. Pure Appl. Algebra, 66, 1990, 229-249. Zbl0716.18003MR1075339
  6. [6] D. Bourn, Mal'cev categories and fibration of pointed objects, Applied Categorical Structures, 4, 1996, 307-327. Zbl0856.18004MR1406105
  7. [7] D. Bourn, Baer sums and fibered aspects of Mal'cev operations, Cahiers de Top. et Géom. Diff. Catégoriques, 40, 1999, 297-316. Zbl0988.18006MR1734248
  8. [8] D. Bourn, Aspherical abelian groupoids and their directions, J. Pure Appl. Algebra, 168, 2002, 133-146. Zbl1015.18001MR1887154
  9. [9] D. Bourn, Baer sums in homological catégories, J. Algebra, 308, 2007, 414-443. Zbl1134.18004MR2290929
  10. [10] D. Bourn and M. Gran, Centrality and connectors in Maltsev categories, Algebra Universalis, 48, 2002, 309-331. Zbl1061.18006MR1954778
  11. [11] A. Carboni, J. Lambek and M.C. Pedicchio, Diagram chasing in Mal'cev categories, J. Pure Appl. Algebra, 69, 1990, 271-284. Zbl0722.18005MR1090744
  12. [12] A. Carboni, M.C. Pedicchio and N. Pirovano, Internal graphs and internal groupoids in Mal'cev categories, Canadian Math.Soc.Conference proceedings, vol.13, 1992, pp. 97-109. Zbl0791.18005MR1192142
  13. [13] J.W. Duskin, Simplicial methods and the interpretation of triple cohomology, Memoirs Amer. Math. Soc., 163, 1975, pp. M R 52/14006. Zbl0376.18011
  14. [14] P.G. Glenn, Realization of cohomology classes in arbitary exact categories, J. Pure Appl. Algebra, 25, 1982, 33-105. Zbl0487.18015MR660389
  15. [15] P. J. Hilton and U. Stammbach, A course in Homological Algebra, Springer, Graduate Texts in Math., 4, 1971. Zbl0238.18006MR346025
  16. [16] D. Holt, An interpretation of the cohomology groups Hn(G,M), J. Algebra, 60, 1979, 307-318. Zbl0699.20040MR549932
  17. [17] J. Huebschmann, Crossed n-fold extensions of groups and cohomology, Comment. Math. Helv., 55, 1980, 302-314. Zbl0443.18019MR576608
  18. [18] P.T. Johnstone, Affine categories and naturally Mal'cev categories, J. Pure Appl. Algebra, 61, 1989, 251-256. Zbl0683.18007MR1027744
  19. [19] S. Mac Lane, Homology, Springer, 1963. MR1344215
  20. [20] D. Rodelo, Direcções para a sucessão longa de co-homologia, Thesis, Coimbra, 2005. 
  21. [21] C.A. Weibel, An introduction to homological algebra, Cambridge Univ. Press, 1994. Zbl0834.18001MR1269324

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