Paper detail

Reduction of wide subcategories and recollements

In this paper, we prove a reduction result on wide subcategories of abelian categories which is similar to Calabi-Yau reduction, silting reduction and $τ$-tilting reduction. More precisely, if an abelian category $\mathcal{A}$ admits a recollement relative to abelian categories $\mathcal{A}&#39;$ and $\mathcal{A}&#34;$, diagrammatically expressed by $$\xymatrix@!C=2pc{ \mathcal{A&#39;} \ar@{>->}[rr]|{i_{*}} && \mathcal{A} \ar@<-4.0mm>@{->>}[ll]_{i^{*}} \ar@{->>}[rr]|{j^{*}} \ar@{->>}@<4.0mm>[ll]^{i^{!}}&& \mathcal{A&#39;&#39;} \ar@{>->}@<-4.0mm>[ll]_{j_{!}} \ar@{>->}@<4.0mm>[ll]^{j_{*}} },$$ then the assignment $\cc\mapsto j^*(\cc)$ defines a bijection between wide subcategories in $\mathcal{A}$ containing $i_{*}(\mathcal{A}&#39;)$ and wide subcategories in $\mathcal{A}&#34;$. Moreover, a wide subcategory $\mathcal{C}$ of $\mathcal{A}$ containing $i_{*}(\mathcal{A}&#39;)$ admits a new recollement relative to $\mathcal{A}&#39;$ and $j^{*}(\mathcal{C})$ which is induced from the original recollement.