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arXiv · 2108.05856

One-sided Frobenius pairs in extriangulated categories

Lingling Tan·Yuqiong Gao·Qinghua Chen
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Abstract

Let $\mathscr{C}$ be an extriangulated category with a proper class $\xi$ 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 $\xi$ 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-P\'{e}rez-Santiago's results in abelian categories.

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Lingling Tan, Yuqiong Gao, Qinghua Chen. 2021-08-12. One-sided Frobenius pairs in extriangulated categories. https://arxiv.org/abs/2108.05856

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