Homological algebra of quiver bundles

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  • 4 February 2002
Abstract
The category of representations of a finite quiver in the category of sheaves of modules on a ringed space is abelian. We show that this category has enough injectives by constructing an explicit injective resolution. From this resolution we deduce a long exact sequence relating the Ext groups in these two categories. We also show that under some hypotheses, the Ext groups are isomorphic to certain hypercohomology groups.

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