Mutation of representations and nearly Morita equivalence

Abstract

ABSTRACTIn Buan et al. [4], it was proved, based on Derksen et al. [5], that the Jacobian algebra of two quivers with potential related by a QP-mutation is nearly Morita equivalent. They proved, using Axiom of Choice, that the natural functor μk is an equivalence by showing that μk is full, faithful and dense. In this note we provide a quasi-inverse to μk without Axiom of Choice.