Representations of quivers on abelian categories and monads on projective varieties

Abstract

We consider representations of quivers in arbitrary categories and twisted representations of quivers in arbitrary ten- sor categories. We show that if A is an abelian category, then the category of representations of a quiver in A is also abelian, and that the category of twisted linear representations of a quiver is equivalent to the category of linear (untwisted) representations of a dierent quiver. We conclude by discussing how represen- tations of quivers arise naturally in certain important problems concerning monads ans sheaves on projective varieties.