Generator coalgebras are not necessarily quasi-coFrobenius
Abstract
We 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 kn:coalgen. We also prove it is true for monomial pointed coalgebras and we characterize the quivers Q such that Q admits a monomial subcoalgebra that is left (right) quasi-coFrobenius.
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