论文标题
添加性Grothendieck自制和张量类别的演示
Additive Grothendieck pretopologies and presentations of tensor categories
论文作者
论文摘要
我们定义了在preadive类别上的概念，该概念扮演的角色类似于毫无增长的类别的Grothendieck Progopology概念。每种此类添加剂自制学都定义了添加剂Grothendieck拓扑结构，并且足以定义捆出类别。这个新的概念使我们能够研究拓扑的Noetherian和子环境性质，可以轻松地描述拓扑家族的相遇并确定捆类类别的有用通用性能。作为我们的主要应用程序，我们得出了哪种方式可以提出张量类别并表明这种演示导致了非凡的通用属性。
We define a notion on preadditive categories which plays a role similar to the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology defines an additive Grothendieck topology and suffices to define the sheaf category. This new notion allows us to study the noetherian and subcanonical nature of topologies, to describe easily the meet of a family of topologies and to identify useful universal properties of the sheaf category. As our main application we derive in which ways one can present a tensor category and show that such presentations lead to remarkable universal properties.
