论文标题
内部自然变换和德林菲尔德中心的Frobenius代数
Internal natural transformations and Frobenius algebras in the Drinfeld center
论文作者
论文摘要
对于有限张量C类别的M和N有限模块类别，正确的精确模块函子的类别REX_C（M，N）是Drinfeld中心Z（c）上的有限模块类别。我们研究了该模块类别的内部HOMS，我们称之为内部自然变换。在某些集成函数的帮助下，将C-C-bimodule函子映射到Z（c）的对象，我们将其表示为内部HOMS的末端，并定义水平和垂直组成。我们表明，如果m和n是精确的C模块，并且C是关键的，则Z（C）-Module REX_C（M，N）是精确的。我们计算其相对Serre函数，并表明如果M和N是关键模块类别，则REX_C（M，N）也是关键的。然后，它的内部是Z（c）中Frobenius代数的丰富来源。
For M and N finite module categories over a finite tensor category C, the category Rex_C(M,N) of right exact module functors is a finite module category over the Drinfeld center Z(C). We study the internal Homs of this module category, which we call internal natural transformations. With the help of certain integration functors that map C-C-bimodule functors to objects of Z(C), we express them as ends over internal Homs and define horizontal and vertical compositions. We show that if M and N are exact C-modules and C is pivotal, then the Z(C)-module Rex_C(M,N) is exact. We compute its relative Serre functor and show that if M and N are even pivotal module categories, then Rex_C(M,N) is pivotal as well. Its internal Ends are then a rich source for Frobenius algebras in Z(C).
