When is a coalgebra a generator?

Let C be a coalgebra over a field k. The aim of this paper is to study the following problem : (P) If C is a k-coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical series, the answer is positive.

Publication year:2008