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A long exact sequence in non-abelian cohomology

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Category Theory

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References

  1. M. Barr, J. Beck. Homology and standard constructions, Lecture Notes in Math.80, Springer-Verlag (1969), 245–335.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Brown. Same non abelian methods in homotopy theory and homological algebia, in Categarical Jopology Proc. Conf. Joledo, Ohio, 1983, ed. H.L. Bentley, et.al., Heldermann-Verlag, Berlin (1984), 108–146.

    Google Scholar 

  3. R. Brown. Fibrations of Groupaids, Journal of Algebra 15 (1970), 103–132.

    Article  MathSciNet  Google Scholar 

  4. R. Brown, N.D. Gilbert. Algebraic models of 3-types and automorphisms atructure for crassed modules, Proc. London Math. Soc. (3) 59 (1989), 51–73.

    Article  MathSciNet  Google Scholar 

  5. A.M. Cegarra, M. Bullejos. Cohomology and higher dimensional Baer invariants, Journal of Algebra 132 (2), (1990), 321–339.

    Article  MathSciNet  MATH  Google Scholar 

  6. A.M. Cegarra, M. Bullejos, A.R. Garzón, Higher dimensional abstruction theory in algebraic categories, Journal of Pure and Applied Algebra 49 (1987), 43–102.

    Article  MathSciNet  MATH  Google Scholar 

  7. A.M. Cegarra, A.R. Garzon, Non-abelian cohomology of associative Algebras. The 9-term exact sequence, Cahiers Top. et Geom. Diff. Catégoriques, vol XXX-4, (1989), 295–338.

    MathSciNet  MATH  Google Scholar 

  8. E.B. Curtis, Jimplicial homotopy theory, Advances in Mathe. 6 (1971), 107–209.

    Article  MathSciNet  Google Scholar 

  9. P. Dedecker, Sur la n-cohomologie non abelienne, C.R. Acad. Sc. Paris, t. 260, 1 (1965), 4137–4139.

    MathSciNet  MATH  Google Scholar 

  10. P. Dedecker, Cohomologie non-abelienne, Mimeographie, Fac. Sc. Lille, 1965.

    Google Scholar 

  11. P. Dedecker, Three dimensional non abelian cohomology for groups, Lecture Notes in Math. 92, Springer-Verlag (1969), 32–64.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. Dedecker, A.S.T. Lue, A non-abelian 2-dimensional cohomology for associative algebras, Bull. A.M.S. 72, (1966), 1044–1050.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Duskin, Simplicial methods and the interpretation of triple cohomology. Memoir A.M.S. vol 3, issue 2, 163 (1975).

    MathSciNet  MATH  Google Scholar 

  14. J.Duskin, Non-abelian monadic cohomology and low dimensional abstruction theory. Math. Forschung Ins. Oberwolfach Tagungsbericht 33, (1976).

    Google Scholar 

  15. J.Duskin, Group cohomology and torsors, Mimeographed notes. (1984).

    Google Scholar 

  16. G.J. Ellis, Crassed modules and their higher dimensional analogues, Ph.D. thesis. Univ. of Wales (1984).

    Google Scholar 

  17. P. Glenn, Realigation of cohomology classes in arbitrary exact categories, Journal of Pure and Applied Algebra 1, 33–107, (1982).

    Article  MathSciNet  MATH  Google Scholar 

  18. P.J.Higgins, Categories and groupoids, Van Nostrand Reinhold Math. Estudes 32 (1971)

    Google Scholar 

  19. P.J. Higgins, Groups with multiple operators. Proc. London Math. Soc. 6, (1956), 366–416.

    Article  MathSciNet  MATH  Google Scholar 

  20. D. Kan, On homotopy theory and c.s.s. groups, Annals of Math. 68, 1 (1958), 38–53.

    Article  MathSciNet  Google Scholar 

  21. F.Keune, Homotopical algebra and algebraic K-theory, Thesis Univ. of Amsterdam (1972).

    Google Scholar 

  22. R. Lavendhomme, J.R. Roisin, Cohomologie non abelienne de structures algebriques. J. of Algebra 67 (1980), 385–414.

    Article  MathSciNet  MATH  Google Scholar 

  23. J.-L. Loday, Spaces with finitely many non trivial homotopy groups, J. of Pure and Applied Algebra 24 (1982), 179–202.

    Article  MathSciNet  MATH  Google Scholar 

  24. A.S.T. Lue, Non-abelian cahamology of assaciative algebras, J. Math. Oxford (2) 19, (1968), 159–180.

    Article  MathSciNet  Google Scholar 

  25. A. S.-T. Lue, Cohomology of groups relative to a variety, J. of Algebra 69 (1981), 155–174.

    Article  MathSciNet  MATH  Google Scholar 

  26. J.P. May, Simplicial objects in Algebraic Japology, Van Nostrand, (1976).

    Google Scholar 

  27. T. Porter, Extensions, crassed modules and internal categories in categories of groups with aperations. Edinburgh Math. Soc. 30, (1987), 415–429.

    Article  Google Scholar 

  28. D. Quillen, Hamatopical Algebra Lecture Notes in Math. 43, Springer-Verlag (1967).

    Google Scholar 

  29. J.P. Van Deuren, Etude de l'abstruction au relevement d'un cocycle non abelien. Essai d'une delinition d'une 3-cohomologie non abelienne, Seminaire de mathematique pure, Univ. Catholique de Louvaine (1978).

    Google Scholar 

  30. J.H.C. Whitehead, Combinatonial homotopy, II, Bull. A.M.S. 55, (1949), 496–543.

    MATH  Google Scholar 

  31. G.W. Whitehead, Elements of homotopy theory, Springer-Verlag (1978).

    Google Scholar 

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Aurelio Carboni Maria Cristina Pedicchio Guiseppe Rosolini

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© 1991 Springer-Verlag

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Cegarra, A.M., Garzón, A.R. (1991). A long exact sequence in non-abelian cohomology. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084214

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  • DOI: https://doi.org/10.1007/BFb0084214

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  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

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