On the existence of recollements of functor categories

Abstract

A sufficient condition for the existence of recollements of functor categories is provided. Using this criterion, we show that a recollement of rings induces a recollement of their path rings (resp. incidence rings, monomial rings) over a locally finite quiver. Also, we present a covering technique for recollement of derived categories of functor categories.

Keywords:

• Functor category
• derived category
• orbit category
• recollement

2010 Mathematics Subject Classification:

• 18E30
• 16E35
• 16G10

Acknowledgments

I would like to thank the referee for her/his comments and hints that improved our exposition. Part of this work is carried out in University of Verona, Italy, when I was visiting there. I would like to thank Professor Lidia Angeleri Hügel for useful discussions and comments.