manuscripta mathematica

, Volume 2, Issue 1, pp 49–66

On generators and cogenerators


  • Bodo Pareigis
    • Mathematisches Institut der Universität
    • Dept. of MathematicsWhite Hall Cornell University
  • Moss E. Sweedler
    • Dept. of MathematicsWhite Hall Cornell University

DOI: 10.1007/BF01168479

Cite this article as:
Pareigis, B. & Sweedler, M.E. Manuscripta Math (1970) 2: 49. doi:10.1007/BF01168479


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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© Springer-Verlag 1969