论文标题
Auslander的公式和确切类别的通信
Auslander's formula and correspondence for exact categories
论文作者
论文摘要
澳大利亚的对应关系是奥斯兰德 - 雷森理论的基本结果。在本文中，我们介绍了类别$ \ permatatorName {mod _ {\ mathsf {adm}}}}}（\ Mathcal {e}）$ forcyscompassency有限地呈现的函数，并使用它给出任何确切类别$ \ mathcal $ \ nathcal {e} $的Auslander对应版本。证明中的重要成分是确切类别的本地化理论。我们还研究了$ \ Mathcal {e} $的属性如何反映在$ \ operatatorName {mod _ {\ mathsf {admsf {adm}}}}}}}}}（\ Mathcal {e}）$中，例如（弱）IDEMPOTENT完整或具有足够的预测或具有足够的预测性或注射性。 Furthermore, we describe $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ as a subcategory of $\operatorname{mod}(\mathcal{E})$ when $\mathcal{E}$ is a resolving subcategory of an abelian category.这包括Gorenstein投射模块的类别和最大Cohen-Macaulay模块的类别。最后，我们使用$ \ operatorName {mod _ {\ mathsf {admsf {adm}}}}（\ Mathcal {e}）$在idempotent完整的添加类别$ \ MATHCAL {C} $上的精确结构之间进行两次射击，并进行$ \ operatornorneorn $ \ operatateRneorn $ {ca）（c）（c）（c）（c）。
The Auslander correspondence is a fundamental result in Auslander-Reiten theory. In this paper we introduce the category $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ of admissibly finitely presented functors and use it to give a version of Auslander correspondence for any exact category $\mathcal{E}$. An important ingredient in the proof is the localization theory of exact categories. We also investigate how properties of $\mathcal{E}$ are reflected in $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$, for example being (weakly) idempotent complete or having enough projectives or injectives. Furthermore, we describe $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ as a subcategory of $\operatorname{mod}(\mathcal{E})$ when $\mathcal{E}$ is a resolving subcategory of an abelian category. This includes the category of Gorenstein projective modules and the category of maximal Cohen-Macaulay modules as special cases. Finally, we use $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ to give a bijection between exact structures on an idempotent complete additive category $\mathcal{C}$ and certain resolving subcategories of $\operatorname{mod}(\mathcal{C})$.
