manuscripta mathematica

, Volume 2, Issue 1, pp 49–66

On generators and cogenerators

  • Bodo Pareigis
  • Moss E. Sweedler
Article

Abstract

We consider the existence of generators and cogenerators in several categories. In many cases the non-existence of cogenerators results from the construction of arbitrarily high dimensional simple (restricted) Lie algebras. The existence of generators in the Hopf algebra categories results from the existence of generators in a certain coalgebra category and the construction of a free Hopf algebra on a coalgebra.

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References

  1. [1]
    GABRIEL, P.: SGA Demazure-Grothendieck 1962/64, Exposée VIIB.Google Scholar
  2. [2]
    HEYNEMAN, R. and M. SWEEDLER: Affine Hopf Algebras. (to appear in J. of Algebra)Google Scholar
  3. [3]
    PAREIGIS, B.: Kategorien und Funktoren. Stuttgart: Teubner 1969.Google Scholar
  4. [4]
    ROTMAN, J.: Theory of Groups. Boston: Allyn and Bacon. 1965Google Scholar
  5. [5]
    Séminaire Heidelberg-Strasbourg 1965/66: Groupes Algébriques Linéaires. Publication I.R.M.A. Strasbourg No-2-1967.Google Scholar
  6. [6]
    SWEEDLER, M.: Hopf Algebras. (to appear: New York-Amsterdam: W.A. Benjamin)Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Bodo Pareigis
    • 1
    • 2
  • Moss E. Sweedler
    • 2
  1. 1.Mathematisches Institut der Universität8 München 13
  2. 2.Dept. of MathematicsWhite Hall Cornell UniversityIthacaUSA

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