Advertisement

manuscripta mathematica

, Volume 2, Issue 3, pp 203–239 | Cite as

Satelliten; Singuläre Erweiterungen und Derivationen

  • Horst Brinkmann
Article

Abstract

This paper is divided in two parts. In chapter one we generalize the concept of satellite for abelian categories, substituting Ext by an arbitrary functor E:Aop×BEns. A very close relation to Kan functor extensions turns out. In chapter two we give a comprehensive formulation of the wellknown cohomology theories for groups and algebras-with the recently used modification in taking the group of derivations as the lowest cohomology group- starting with a categorical definition of the concept of singular extension. There is a zeroth chapter with a construction on functors, needed in both parts, and a third with examples.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literatur

  1. [1]
    Beck, J.M.: Triples, Algebras and Cohomology. Dissertation, Columbia University 1967Google Scholar
  2. [2]
    Buchsbaum, D.A.: A note on homology in Categories. Ann. of Math. II. Ser. 69, 66–74 (1959)Google Scholar
  3. [3]
    Buchsbaum, D.A.: Satellites and universal functors. Ann. of Math. II. Ser. 71, 199–209 (1960)Google Scholar
  4. [4]
    Buchsbaum, D.A.: Homology and universality relative to a functor. 1967Google Scholar
  5. [5]
    Cartan, H. u. S. Eilenberg: Homological Algebra. Princeton, New Jersey: Princeton University Press 1956Google Scholar
  6. [6]
    Dold, A.: Halbexakte Homotopiefunktoren. Lecture Notes in Math. 12, Berlin-Heidelberg-New York: Springer 1966Google Scholar
  7. [7]
    Eilenberg, S.: Extensions of general algebras. Ann. Soc. Polon. Math. 21, 125–134 (1948)Google Scholar
  8. [8]
    Fisher, J.L.: The Tensor Product of Functors; Satellites; and Derived Functors. J. Algebra 8, 277–294 (1968)Google Scholar
  9. [9]
    Gray, J.W.: Fibred and Cofibred Categories. Proc. Conf. Cat. Alg., La Jolla 1965. Berlin-Heidelberg-Hew York: Springer 1966Google Scholar
  10. [10]
    Grothendieck, A.: Catégories Fibrées et Descente. Inst. haut. Etud., Sém. Géo. Alg. 1960–1961. Paris 1961Google Scholar
  11. [11]
    Mac Lane, S.: Homology. Berlin-Heidelberg-New York: Springer 1963Google Scholar
  12. [12]
    Mac Lane, S.: Natural associativity and commutativity. Rice Univ. Studies 49, Nr. 4, 28–46 (1963)Google Scholar
  13. [13]
    Mac Lane, S.: Categorical algebra. Bull. Amer. Math. Soc. 71, 40–106 (1965)Google Scholar
  14. [14]
    Mitchell, B.: Theory of Categories. New York: Acad. Press 1965Google Scholar
  15. [15]
    Serre, J.P.: Cohomology Galoisienne. Lecture Notes in Math. 5, Berlin-Heidelberg-New York: Springer 1964Google Scholar
  16. [16]
    Ulmer, F.: On Kan Functor Extensions. Forschungsinstitut für Math., ETH Zürich, 1966Google Scholar
  17. [17]
    Yoneda, N.: On Ext and exact sequences. J. Fac. Sci. Univ. Tokyo, Sect. I, 8, 507–576 (1960)Google Scholar

Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Horst Brinkmann
    • 1
  1. 1.Wolfartsweier

Personalised recommendations