Presilting sequences for 0-Auslander extriangulated categories

Abstract

Let $\mathcal{C}$ be a reduced $0$-Auslander extriangulated category. Motivated by Pan--Zhu silting reduction for such categories, we introduce the notion of (signed) presilting sequences in $\mathcal{C}$ and establish a bijection between (signed) presilting sequences in $\mathcal{C}$ and (signed) $\ddot{I}„$-exceptional sequences over $\hat{I}›={\text{End}}_{\mathcal{C}}(P)$, where $P$ is a projective generator of $\mathcal{C}$. This correspondence provides a new perspective on the Buan--Marsh bijection between signed $\ddot{I}„$-exceptional sequences and ordered support $\ddot{I}„$-rigid objects. Furthermore, we introduce a new category $\mathfrak{M}(\mathcal{C})$, called the $\ddot{I}„$-cluster morphism category of $\mathcal{C}$, whose objects are certain extension-closed subcategories of $\mathcal{C}$ and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the $\ddot{I}„$-cluster morphism category of $\hat{I}›$ from $\mathfrak{M}(\mathcal{C})$.

38 pages. Comments are welcome!