Generator coalgebras are not necessarily quasi-coFrobenius

2008/09/25 by Mariana Haim, Haim, Mariana, Blas Torrecillas +1
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.0809.4410

arxiv created 2009/03/17 · arxiv updated 2009/12/01

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 \citekn: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.

Related

• Cofrobenius Coalgebra
• Generators for comonoids and universal constructions
• Homotopy Theory of linear coalgebras
• Localization in coalgebras. Applications to finiteness conditions
• Comodules and contramodules over coalgebras associated with locally finite categories