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