TCDMATH 18--19: Quiver representations in Abelian categories, by Sergey Mozgovoy

Abstract. We introduce the notion of (twisted) quiver representations in abelian cate- gories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological properties of the category of representations. These results are applied in the case of parabolic vector bundles and framed coherent sheaves.