论文标题
Abelian类别图的表示形式I：全球结构和同源对象
Representations over diagrams of abelian categories I: Global structure and homological objects
论文作者
论文摘要
阿贝利亚类别图表的表示形式统一了很多概念，在文献中广泛出现，例如类别的表示，模块的预示，类别，物种的表示等。在这一系列论文中，我们会系统地研究它们，表征在表示类别中的特殊同源对象以及在各种结构（例如模型结构和Wandhuasen cartery类别）中的特殊同源对象。在第一篇论文中，我们调查了表示类别的Grothendieck结构，描述重要的函数和邻接关系，并表征特殊的同源对象。这些结果为我们未来的作品奠定了基础。
Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of papers we study them systematically, characterizing special homological objects in representation category and constructing various structures (such as model structures and Wandhuasen category strcutres) on it. In the first paper we investigate the Grothendieck structure of the representation category, describe important functors and adjunction relations between them, and characterize special homological objects. These results lay a foundation for our future works.
