Tilting theory provides a good method for comparing two categories, such as module categories of finite-dimensional algebras. For an introduction, see e.g. [A]. BGP reflection functors [BGP] give a way of comparing the representation categories of two quivers, where one is obtained from the other by reversing all of the arrows incident with a sink or source. Auslander, Platzeck and Reiten [APR] showed that the BGP reflection functors can be realised directly as functors of the form Hom(T, −), where T is an APR-tilting module. In cluster–tilting theory [BMR1, BMR2, BMRRT] APR-tilting theory has been generalised to cover arbitrary vertice
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