论文标题
三角剖分类别的二元性对，幻影图和确定性
Duality pairs, phantom maps, and definability in triangulated categories
论文作者
论文摘要
我们在紧凑的三角类别中定义了双重性和二元性对并研究它们的性质。这使我们能够提供一种基本的方法来确定在纯对象，纯商和纯扩展中是否关闭一类，并提供一种显示近似值存在的方法。一种关键成分是幻影图的新表征。然后，我们引入了Auslander-Gruson-Jensen双重性的公理形式，从中定义了双重定义类别，并证明这些类别与对称共同的闭合双重性对一致。该框架无处不在，包括代数三角剖分类别和稳定的同型理论。因此，我们在这两种环境中都提供了许多应用，并特别强调淤积理论和分层的张量三角类别。
We define duality triples and duality pairs in compactly generated triangulated categories and investigate their properties. This enables us to give an elementary way to determine whether a class is closed under pure subobjects, pure quotients and pure extensions, as well as providing a way to show the existence of approximations. One key ingredient is a new characterisation of phantom maps. We then introduce an axiomatic form of Auslander-Gruson-Jensen duality, from which we define dual definable categories, and show that these coincide with symmetric coproduct closed duality pairs. This framework is ubiquitous, encompassing both algebraic triangulated categories and stable homotopy theories. Accordingly, we provide many applications in both settings, with a particular emphasis on silting theory and stratified tensor-triangulated categories.
