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Title: Abelian Hall categories
After reviewing some background, we will explain how to associate to any
quiver a finite length abelian category which categorifies the
corresponding K-theoretic Hall algebra. The simples in this category
provide a (dual) canonical basis of the Hall algebra. In particular, if
the quiver is affine, this provides a basis for the positive half of the
corresponding quantum toroidal algebra. We also explain how this abelian
category is naturally endowed with renormalized r-matrices.
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