Abstract
Let D be a triangulated category with a cluster tilting subcategory U . The quotient category D / U is abelian; suppose that it has finite global dimension. We show that projection from D to D / U sends cluster tilting subcategories of D to support tilting subcategories of D / U , and that, in turn, support tilting subcategories of D / U can be lifted uniquely to weak cluster tilting subcategories of D .
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