Presilting sequences for 0-Auslander extriangulated categories
Abstract
Let be a reduced -Auslander extriangulated category. Motivated by Pan--Zhu silting reduction for such categories, we introduce the notion of (signed) presilting sequences in and establish a bijection between (signed) presilting sequences in and (signed) -exceptional sequences over , where is a projective generator of . This correspondence provides a new perspective on the Buan--Marsh bijection between signed -exceptional sequences and ordered support -rigid objects. Furthermore, we introduce a new category , called the -cluster morphism category of , whose objects are certain extension-closed subcategories of and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the -cluster morphism category of from .
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!