标题： 单性范畴的仿射化 显示英文标题

标题： Affinization of monoidal categories

摘要： 我们定义任意单子范畴$\mathcal{C}$的仿射化，对应于圆柱体上的$\mathcal{C}$图形的范畴。 我们还通过向$\mathcal{C}$添加点生成元来给出另一种描述。 仿射化形式化并统一了许多文献中出现的构造。 特别是，我们描述了来自 Hecke 类代数、辫子、扭结和纽结不变量的大量例子。 当$\mathcal{C}$是刚性的时，其仿射化与它的水平迹同构，尽管这两个定义看起来差别很大。 一般来说，仿射化和水平迹不是同构的。 显示英文摘要

摘要： 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.