We show that the quotient of a Hom-finite triangulated category by the kernel of the functor Hom(T,-), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admits a calculus of left and right fractions. It follows that the Gabriel-Zisman localization of the quotient at the class of regular morphisms is abelian. We show that it is equivalent to the category of finite-dimensional modules over the opposite of the endomorphism algebra of T in.
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