2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223337We study the problem of whether a coalgebra that generates its category of left (right) comodules is left (right) quasi-coFrobenius or not. We prove it does not hold in general, by giving a method of constructing counterexamples. This gives a negative answer to a question stated in \cite{kn:coalgen}. We also prove it is true for monomial pointed coalgebras and we characterize the quivers $Q$ such that $\Bbbk Q$ admits a monomial subcoalgebra that is left (right) quasi-coFrobenius.Rings and AlgebrasQuantum Algebratext