论文标题
稳定的函子和同步学理论
Stable functors and cohomology theory in abelian categories
论文作者
论文摘要
在本文中，我们首先针对预先开发/定制子类别引入稳定的函子，并研究它们的某些属性。然后，我们介绍并研究了阿贝尔类别中的相对完整的共同体学理论。赋予了包括消失在内的共同体学的某些特性。作为应用，我们给出了有限同源尺寸的对象的一些特征，包括扁平尺寸，cotorsion尺寸，戈伦斯坦注射/扁平尺寸以及核心核化的Gorenstein Flat Vimension。
In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian categories. Some properties of the cohomology including vanishing are given. As applications, we give some characterizations of objects of finite homological dimensions including the flat dimension, cotorsion dimension, Gorenstein injective/flat dimension and projectively coresolved Gorenstein flat dimension.
