论文标题
半纤维类别类别
Semibricks in extriangulated categories
论文作者
论文摘要
令$ \ mathcal {x} $为外部策略类别$ \ mathscr {c} $中的半成品。令$ \ mathcal {t} $为$ \ Mathcal {x} $生成的过滤子类别。我们在$ \ mathscr {c} $中给出了简单的半键和长度宽子类别之间的一对一对应关系。这概括了Ringel在模块类别中给出的两者，该模块类别已通过Inomoto推广到确切类别。此外，我们还在$ \ Mathcal {t} $的cotorsion对与$ \ Mathcal {x} $的某些子集之间提供一对一的对应关系。应用于三角形类别的简单智力系统，我们恢复了Dugas给出的结果。
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.
