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THE RESOLUTION DIMENSIONS WITH RESPECT TO BALANCED PAIRS IN THE RECOLLEMENT OF ABELIAN CATEGORIES

Fu, Xuerong;Hu, Yonggang;Yao, Hailou

  • Received : 2018.08.25
  • Accepted : 2019.01.24
  • Published : 2019.07.01

Abstract

In this paper we study recollements of abelian categories and balanced pairs. The main results are: recollements induce new balanced pairs from the middle category; the resolution dimensions are bounded under certain conditions. As an application, the resolution dimensions with respect to cotilting objects of abelian categories involved in recollements are recovered.

Keywords

recollement;resolution dimension;balanced pair

Acknowledgement

Supported by : National Natural Science Foundation of China