Some constructions of abelian or triangulated categories
报告摘要：Abelian categories and triangulated categories are two fundamental structures in mathematics. The semisimple categories are the only categories whichare abelian and triangulated. One can form complexes from abelian categories to get homotopy categories, and then derived categories by localization, which are triangulated. One can also get abelian categories by forming the hearts of t-structures in the triangulated categories.
In this talk, we will recall the classical constructions of abelian or triangulated categories, and then to survey the "new" constructions which arising from the study of cluster tilting theory and cluster algebras.