We introduce the notion of (twisted) quiver representations in abelian categories 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.
Generalized associahedra via quiver representations
Laurent expansions in cluster algebras via quiver representations
The Combinatorics of Quiver Representations
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