Silting objects and recollements of extriangulated categories

Zhen Zhang; Shance Wang; Zhen Zhang; Shance Wang

doi:10.3934/math.20241207

AIMS Mathematics

2024, Volume 9, Issue 9: 24796-24809. doi: 10.3934/math.20241207

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Research article

Silting objects and recollements of extriangulated categories

Zhen Zhang ,
Shance Wang ^,

Department of Mathematics, Qilu Normal University, Ji'nan 250200, China

Received: 03 April 2024 Revised: 15 August 2024 Accepted: 19 August 2024 Published: 23 August 2024
MSC : 16G10, 18E40, 18G80

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.
- extriangulated category,
- recollement,
- silting object,
- tilting object,
- cotorsion pair
Citation: Zhen Zhang, Shance Wang. Silting objects and recollements of extriangulated categories[J]. AIMS Mathematics, 2024, 9(9): 24796-24809. doi: 10.3934/math.20241207

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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.

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