论文标题
外部的理想商和Gabriel-Zisman的本地化
Extriangulated ideal quotients and Gabriel-Zisman localizations
论文作者
论文摘要
令$（\ Mathcal B，\ Mathbb {e}，\ Mathfrak {s}）$为外侧类别，$ \ Mathcal s $为$ \ Mathcal b $的扩展封闭子类别。在本文中，我们证明了Gabriel-Zisman本地化$ \ Mathcal B/\ Mathcal S $可以实现为$ \ Mathcal B $内部的理想商，当$ \ Mathcal S $满足某些温和条件。理想的商是外侧类别。我们表明，理想商和本地化之间的等效性保留了外侧类别结构。我们还讨论了结果与Hovey Twin Cotorsion对和Verdier商的关系。
Let $(\mathcal B,\mathbb{E},\mathfrak{s})$ be an extriangulated category and $\mathcal S$ be an extension closed subcategory of $\mathcal B$. In this article, we prove that the Gabriel-Zisman localization $\mathcal B/\mathcal S$ can be realized as an ideal quotient inside $\mathcal B$ when $\mathcal S$ satisfies some mild conditions. The ideal quotient is an extriangulated category. We show that the equivalence between the ideal quotient and the localization preserves the extriangulated category structure. We also discuss the relations of our results with Hovey twin cotorsion pairs and Verdier quotients.
