论文标题
相对单调的分配法律
Distributive laws for relative monads
论文作者
论文摘要
我们介绍了相对单调和单子之间的分配法律的概念。我们将其称为相对分布定律，并在任何2类别$ \ MATHCAL {K} $中定义它。为此，我们将相对单调的2类相对单调介绍在2类$ \ Mathcal {k} $中，分别为1和2细胞。我们将我们的定义与$ \ Mathcal {k} $的2类monads联系起来。多亏了这种观点，我们证明了有关相对分布定律的两个贝克型定理。我们还描述了在这种情况下将eilenberg-moore和kleisli对象的eilenberg-moore和kleisli对象的含义，并在本地小型类别的2类中提供示例。
We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category $\mathcal{K}$. In order to do that, we introduce the 2-category of relative monads in a 2-category $\mathcal{K}$ with relative monad morphisms and relative monad transformations as 1- and 2-cells, respectively. We relate our definition to the 2-category of monads in $\mathcal{K}$ defined by Street. Thanks to this view we prove two Beck-type theorems regarding relative distributive laws. We also describe what does it mean to have Eilenberg-Moore and Kleisli objects in this context and give examples in the 2-category of locally small categories.
