外三角范畴中的单侧Frobenius对
One-sided Frobenius pairs in extriangulated categories
摘要：
设$\mathscr{C}$是一个外三角范畴，其真类$ξ$为$\mathbb{E}$ -三角形.在$\mathscr{C}$中引入了关于$ξ$的左Frobenius对、左（$n$ -）余扭对和左（弱）Auslander-Buchweitz上下文的概念.我们展示了如何从左$n$ -余扭对构造左余扭对，并在左Frobenius对和左（弱）Auslander-Buchweitz上下文之间建立一一对应。我们还研究了一类余挠对与$n$ -余挠对的关系。这些工作推广了马兆黄在三角范畴中的结果，并部分推广了Becerril-Mendoza-Pérez-Santiago在阿贝尔范畴中的结果。
英文摘要：
Let $\mathscr{C}$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles. We introduce the notions of left Frobenius pairs, left ($n$-)cotorsion pairs and left (weak) Auslander-Buchweitz contexts with respect to $ξ$ in $\mathscr{C}$. We show how to construct left cotorsion pais from left $n$-cotorsion pairs, and establish a one-to-one correspondence between left Frobenius pairs and left (weak) Auslander-Buchweitz contexts. We also study the relation between a certain class of cotorsion pairs and that of $n$-cotorsion pairs. These work generalize Ma-Zhao-Huang's results in triangulated categories and partially generalize Becerril-Mendoza-Pérez-Santiago's results in abelian categories.
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