Mutation of representations and nearly Morita equivalence

摘要

In 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 (k) is an equivalence by showing that (k) is full, faithful and dense. In this note we provide a quasi-inverse inline-graphinline-graphic to (k) without Axiom of Choice.