English

Presilting sequences for 0-Auslander extriangulated categories

Representation Theory 2026-05-21 v1

Abstract

Let C\mathscr{C} be a reduced 00-Auslander extriangulated category. Motivated by Pan--Zhu silting reduction for such categories, we introduce the notion of (signed) presilting sequences in C\mathscr{C} and establish a bijection between (signed) presilting sequences in C\mathscr{C} and (signed) τ\tau-exceptional sequences over Λ=EndC(P)\Lambda = \text{End}_{\mathscr{C}}(P), where PP is a projective generator of C\mathscr{C}. This correspondence provides a new perspective on the Buan--Marsh bijection between signed τ\tau-exceptional sequences and ordered support τ\tau-rigid objects. Furthermore, we introduce a new category M(C)\mathfrak{M}(\mathscr{C}), called the τ\tau-cluster morphism category of C\mathscr{C}, whose objects are certain extension-closed subcategories of C\mathscr{C} and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the τ\tau-cluster morphism category of Λ\Lambda from M(C)\mathfrak{M}(\mathscr{C}).

Keywords

Cite

@article{arxiv.2605.20957,
  title  = {Presilting sequences for 0-Auslander extriangulated categories},
  author = {Iacopo Nonis},
  journal= {arXiv preprint arXiv:2605.20957},
  year   = {2026}
}

Comments

38 pages. Comments are welcome!

R2 v1 2026-07-22T07:23:37.223Z