Recollements of thick subcategories

Yuxia Mei, Li Wang, Jiaqun Wei

Published 2024-09-27Version 1

Let $(\mathcal{A}, \mathcal{B}, \mathcal{C}, i^{*}, i_{\ast}, i^{!},j_!, j^\ast, j_\ast)$ be a recollement of extriangulated categories. We show that there is a bijection between thick subcategories in $\mathcal{C}$ and thick subcategories in $\mathcal{B}$ containing $i_{\ast}\mathcal{A}$. Futhermore, the thick subcategories $\mathcal{V}$ in $\mathcal{B}$ containing $i_{\ast}\mathcal{A}$ can induce a new recollement relative to $\mathcal{A}$ and $j^{\ast}\mathcal{V}$. We also prove that silting subcategories in $\mathcal{A}$ and $\mathcal{C}$ can be glued to get silting subcategories in $\mathcal{B}$ and the converse holds under certain conditions.