manuscripta mathematica

, Volume 2, Issue 1, pp 49-66

First online:

On generators and cogenerators

  • Bodo PareigisAffiliated withMathematisches Institut der UniversitätDept. of Mathematics, White Hall Cornell University
  • , Moss E. SweedlerAffiliated withDept. of Mathematics, White Hall Cornell University

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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.