Abstract Let R be an Artin ring and be a family of objects in an Artin extriangulated R-category such that for all In this article, we show that the class of the Θ-projective objects is a precovering class and the class of the Θ-injective objects is a pre-enveloping one in Furthermore, if has enough projectives and enough injectives, we show that the subcategory of Θ-filtered objects is functorially finite in As an application, this generalizes the works by Ringel in a module category case and Mendoza–Santiago in a triangulated category case.

中文翻译：

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外三角化类别中的过滤对象

摘要 令 R 是一个 Artin 环，并且是一个 Artin 外三角化 R 类别中的对象族，使得对于所有在本文中，我们证明 Θ-射影对象的类是一个预覆盖类和 Θ-的类单射对象是一个预先包络的对象此外，如果有足够的射影和足够的单射，我们证明了经过 Θ 过滤的对象的子类别在函数上是有限的 作为一个应用程序，这概括了 Ringel 在模块类别案例和 Mendoza 中的作品–圣地亚哥在三角分类案例中。