English

Semibricks in extriangulated categories

Representation Theory 2020-10-12 v1 Category Theory Rings and Algebras

Abstract

Let X\mathcal{X} be a semibrick in an extriangulated category C\mathscr{C}. Let T\mathcal{T} be the filtration subcategory generated by X\mathcal{X}. We give a one-to-one correspondence between simple semibricks and length wide subcategories in C\mathscr{C}. This generalizes a bijection given by Ringel in module categories, which has been generalized by Enomoto to exact categories. Moreover, we also give a one-to-one correspondence between cotorsion pairs in T\mathcal{T} and certain subsets of X\mathcal{X}. Applying to the simple minded systems of an triangulated category, we recover a result given by Dugas.

Keywords

Cite

@article{arxiv.2010.04393,
  title  = {Semibricks in extriangulated categories},
  author = {Li Wang and Jiaqun Wei and Haicheng Zhang},
  journal= {arXiv preprint arXiv:2010.04393},
  year   = {2020}
}

Comments

19 pages

R2 v1 2026-06-23T19:11:55.139Z