Simple-minded systems and reduction for negative Calabi-Yau triangulated categories
Abstract
We develop the basic properties of w-simple-minded systems in (-w)-Calabi-Yau triangulated categories for w ≥ 1. The main result is a reduction technique for negative Calabi-Yau triangulated categories. We show that the theory of simple-minded systems exhibits striking parallels with that of cluster-tilting objects. Our construction provides an inductive technique for constructing simple-minded systems.
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