论文标题
2类Monads的通用属性是什么？
What is the universal property of the 2-category of monads?
论文作者
论文摘要
对于2类别$ \ MATHCAL {K} $，我们考虑街道的2类Mond（$ \ Mathcal {k} $）单月的$ \ Mathcal {k} $，以及Lavel and Street的2型category em（$ \ \ \ \ \ \ \ varycal {k} $）和Identity-endity-ondity-on-on-on-on-obignts-on-obignts 2-cells-cells-cells-cells-cells-cells-cells-cells 2-cells-cells-cells and-1-cells-cells-cells-1-cell Mnd（$ \ Mathcal {k} $）$ \ to $ em（$ \ Mathcal {k} $）之间。我们表明，该2函数可以作为2函数$ 1 \ COLON \ MATHCAL {K} \ to \ MATHCAL {k} $的“免费完成”。我们通过对2个函数作为对象和1个细胞的身份来实现这一目标，作为类别富含笛卡尔封闭类别$ \ mathbf {bo mathbf {bo} $，其对象是身份 - 对象启用函数。我们还开发了$ \ mathbf {bo} $的一些理论。
For a 2-category $\mathcal{K}$, we consider Street's 2-category Mnd($\mathcal{K}$) of monads in $\mathcal{K}$, along with Lack and Street's 2-category EM($\mathcal{K}$) and the identity-on-objects-and-1-cells 2-functor Mnd($\mathcal{K}$) $\to$ EM($\mathcal{K}$) between them. We show that this 2-functor can be obtained as a "free completion" of the 2-functor $1\colon \mathcal{K} \to \mathcal{K}$. We do this by regarding 2-functors which act as the identity on both objects and 1-cells as categories enriched a cartesian closed category $\mathbf{BO}$ whose objects are identity-on-objects functors. We also develop some of the theory of $\mathbf{BO}$-enriched categories.
