Rigid subcategories and related subcategories in extriangulated categories

Abstract

In this paper, we firstly obtain the analogue of a Bongartz completion for functorially finite rigid subcategories in an extriangulated category and then we investigate the properties of n-cluster tilting subcategories in an extriangulated category for any positive integer n and show some equivalent characterization of them. Particularly, when the extriangulated category is 2-Calabi-Yau, we show any n-cluster tilting subcategories are in fact cluster tilting for any integer $n\ge 2$ and they coincide with strongly contravariantly finite maximal n-rigid subcategories.

Keywords:

• Cluster tilting subcategory
• extriangulated category
• rigid subcategory
• strongly functorially finite subcategory

2020 Mathematics Subject Classification:

• 18E05
• 16D90
• 16G10

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (No. 12101344) and the Shan Dong Provincial Natural Science Foundation of China (No. ZR2015PA001).