Semibricks in extriangulated categories
Representation Theory
2020-10-12 v1 Category Theory
Rings and Algebras
Abstract
Let be a semibrick in an extriangulated category . Let be the filtration subcategory generated by . We give a one-to-one correspondence between simple semibricks and length wide subcategories in . 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 and certain subsets of . Applying to the simple minded systems of an triangulated category, we recover a result given by Dugas.
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