论文标题
单体类别的影响
Affinization of monoidal categories
论文作者
论文摘要
我们定义了一个任意单体类别$ \ MATHCAL {C} $的亲密关系，对应于$ \ Mathcal {C} $ - 圆柱上的图。我们还根据将点发生器与$ \ Mathcal {C} $相邻的替代表征。亲身化正式并统一了文献中出现的许多结构。特别是，我们描述了来自Hecke型代数，辫子，缠结和结的大量示例。当$ \ Mathcal {c} $刚性时，尽管两个定义看起来完全不同，但其效果与其水平跟踪同构相同。通常，启动和水平迹线不是同构。
We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to $\mathcal{C}$. The affinization formalizes and unifies many constructions appearing in the literature. In particular, we describe a large number of examples coming from Hecke-type algebras, braids, tangles, and knot invariants. When $\mathcal{C}$ is rigid, its affinization is isomorphic to its horizontal trace, although the two definitions look quite different. In general, the affinization and the horizontal trace are not isomorphic.
