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