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In this article, we give a definition and a classification of 'higher'simple-minded systems in triangulated categories generated by spherical objectswith negative Calabi-Yau dimension. We also study mutations of this class ofobjects and that of 'higher' Hom-configurations and Riedtmann configurations.This gives an explicit analogue of the nice mutation theory exhibited incluster-tilting theory.

Mutations of simple-minded systems in Calabi-Yau categories generated by a spherical object