Semibricks in extriangulated categories

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 a triangulated category, we recover a result given by Dugas.