Abstract
This paper surveys the constructions of 3-Calabi-Yau triangulated categories with simple-minded collections due to Ginzburg and Kontsevich-Soibelman and the constructionsof 2-Calabi-Yau triangulated categories with cluster-tilting objects due to Buan-Marsh-Reiten-Reineke-Todorov and Amiot, and includes a discussion on the normal form of2-Calabi-Yau triangulated categories with cluster-tilting objects.
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