Presilting sequences for 0-Auslander extriangulated categories

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) $\tau$-exceptional sequences over $\mathrm{\Lambda }={\text{End}}_{\mathcal{C}}(P)$, where $P$ is a projective generator of $\mathcal{C}$. This correspondence provides a new perspective on the Buan–Marsh bijection between signed $\tau$-exceptional sequences and ordered support $\tau$-rigid objects. Furthermore, we introduce a new category $\mathfrak{M}(\mathcal{C})$, called the $\tau$-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 $\tau$-cluster morphism category of $\mathrm{\Lambda }$ from $\mathfrak{M}(\mathcal{C})$.