论文标题
与奥斯兰德 - 布切茨理论和社交理论有关的外部策略类别中的剪切概念
Cut notions in extriangulated categories related to Auslander-Buchweitz theory and cotorsion theory
论文作者
论文摘要
在这项工作中，我们在奥斯兰德 - 布奇威茨理论和交立理论中介绍了外侧类别的概念，这些概念将给定的类别扩展到了阿贝利亚类别。尽管这些概念已经是针对非凡的作品中的外侧类别开发的，但是在本文中，我们通过考虑对象的子类别来以相对意义的方式解决它们。这种方法不仅涵盖了对阿贝尔，精确和三角形类别的现有理论，而且还显示了如何通过对局部特性的适当处理获得相似的结果。
In this work we introduce notions in Auslander-Buchweitz theory and cotorsion theory in extriangulated categories which extend the given ones for abelian categories. Although these notions have been already developed for extriangulated categories in remarkable works, in this paper, we tackle them in a relative sense by considering subcategories of objects. This approach not only covers the existing theory given on abelian, exact and triangulated categories, but it also shows how to get similar results with an appropriate treatment of local properties.
