Thorsten Holm, Peter Jorgensen
Published 2008-10-02Version 1
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 maximal 1-orthogonal subcategories of D.
The singularity category of a $d\mathbb{Z}$-cluster tilting subcategory
Triangulated categories with cluster-tilting subcategories
Two-term relative cluster tilting subcategories, $τ-$tilting modules and silting subcategories
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