The interplay between 2-and-3-Calabi--Yau triangulated categories

2018/11/19 by Dong Yang, Yang, Dong
Mathematics · #14A22 #16E45 #18E30 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1811.07553

openalex publication_date 2018/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On triangulated orbit categories

Related

• Lifting to cluster-tilting objects in 2-Calabi-Yau triangulated categories
• On the structure of Calabi-Yau categories with a cluster tilting subcategory
• Cluster characters for 2-Calabi-Yau Frobenius extriangulated categories
• Silting reduction and Calabi--Yau reduction of triangulated categories
• On a triangulated category which behaves like a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon