Silting objects and recollements of extriangulated categories

Abstract

In this paper, let $ (\mathscr{A}, \mathscr{C}, \mathscr{B}) $ be a recollement of extriangulated categories. We construct a silting object and a tilting object from the two end terms of a recollement. We also show that the reverse direction holds under natural assumptions. Moreover, we show that our gluing preserves cotorsion pairs.

Keywords

• extriangulated category
• recollement
• silting object
• tilting object
• cotorsion pair