Semibricks in extriangulated categories
Abstract
Let $\mathcal{X}$ be a semibrick in an extriangulated category $\mathscr{C}$. Let $\mathcal{T}$ be the filtration subcategory generated by $\mathcal{X}$. We give a one-to-one correspondence between simple semibricks and length wide subcategories in $\mathscr{C}$. 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 $\mathcal{T}$ and certain subsets of $\mathcal{X}$. Applying to the simple minded systems of an triangulated category, we recover a result given by Dugas.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.04393
- arXiv:
- arXiv:2010.04393
- Bibcode:
- 2020arXiv201004393W
- Keywords:
-
- Mathematics - Representation Theory;
- Mathematics - Category Theory;
- Mathematics - Rings and Algebras
- E-Print:
- 19 pages