论文标题
三角形类别中的$σ$ pure Injextitive的特征和内生对象的应用
Characterisations of $Σ$-pure-injectivity in triangulated categories and applications to endoperfect objects
论文作者
论文摘要
我们提供了各种方式来表征紧凑的三角形类别中的$σ$ - pure-pure Injementive对象。这些特征模仿了模块的模型理论。证明涉及两种方法。在第一种方法中，我们从模块理论环境中调整参数。在这里，固定环上模块的单排语言被典型的多组语言取代，其各种语言由紧凑的对象给出。在整个过程中，我们使用Yoneda嵌入的变体，称为RANTARDED YONEDA FOUNDOR，该函数将多组结构与每个对象相关联。第二种方法是使用此函子翻译语句。尤其是，从三角形类别中的$σ$ - 棕榈注射剂是从Grothendieck类别中的$σ$ impontive对象中得出的。结合这两种方法突出了函数类别中发电机的分类PP可定义亚组和歼灭器子对象之间的连接。我们的表征激发了我们所谓的内列对象的引入，从而概括了内福对象。
We provide various ways to characterise $Σ$-pure-injective objects in a compactly generated triangulated category. These characterisations mimic analogous well-known results from the model theory of modules. The proof involves two approaches. In the first approach we adapt arguments from the module-theoretic setting. Here the one-sorted language of modules over a fixed ring is replaced with a canonical multi-sorted language, whose sorts are given by compact objects. Throughout we use a variation of the Yoneda embedding, called the resticted Yoneda functor, which associates a multi-sorted structure to each object. The second approach is to translate statements using this functor. In particular, results about $Σ$-pure-injectives in triangulated categories are deduced from results about $Σ$-injective objects in Grothendieck categories. Combining the two approaches highlights a connection between sorted pp-definable subgroups and annihilator subobjects of generators in the functor category. Our characterisation motivates the introduction of what we call endoperfect objects, which generalise endofinite objects.
