标题： 双幺矩阵 显示英文标题

标题： Duoidal R-Matrices

摘要： 在本短文中，我们定义了在两个张量积上关于单子具有反蒙诺idal性的双代数的R-矩阵类比结构。类似于经典情形，这类结构与单子的Eilenberg--Moore范畴上的双重结构一一对应。此外，我们研究了这种结构的余交换版本如何提升正规双重范畴的线性分布结构。 显示英文摘要

摘要： In this note, we define an analogue of R-matrices for bialgebras in the setting of a monad that is opmonoidal over two tensor products. Analogous to the classical case, such structures bijectively correspond to duoidal structures on the Eilenberg--Moore category of the monad. Further, we investigate how a cocommutative version of this lifts the linearly distributive structure of a normal duoidal category.