Abstract

Let $\mathcal{X}$ be a semibrick in an extriangulated category $\mathcal{C}.$ 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 $\mathit{C}.$ 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 a triangulated category, we recover a result given by Dugas.

中文翻译：

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分三角类别中的半砖

摘要

让 $\mathcal{X}$ 成为外三角范畴中的半砖 $\mathcal{C}.$ 让 $\mathcal{吨}$ 是由生成的过滤子类别 $\mathcal{X}.$ 我们给出了简单半砖和长度宽子类别之间的一一对应关系 $\mathit{C}.$这推广了 Ringel 在模块类别中给出的双射，Enomoto 已将其推广到精确类别。此外，我们还给出了 cotorsion 对之间的一一对应关系$\mathcal{吨}$ 和某些子集 $\mathcal{X}.$ 应用于三角范畴的简单系统，我们恢复了 Dugas 给出的结果。