标题： 递减乘积的导出辫子及其范畴 显示英文标题

标题： Derived Braids of Decreasing Products and their Categories

摘要： 从辫子中导出的辫子已被用于根据辫子对称单体范畴 V 的结构进行分类。具有四股辫子作为在 V 上丰富化的范畴的张量积的复合态射，导出的辫子相等已被看到与 Joyal 和 Street 关于辫子对称单体范畴的一致性结果相对应，即当图的腿所依据的辫子相等时，图是可交换的。 导出辫子的相等可以被视为 Joyal 和 Street 工作中出现的杨-巴克斯特方程的一种推广。 主要结果是对减少乘积的证明，这些减少乘积是由具有偶数股的组件辫子形成的，它们具有等价的导出辫子。 未来工作的计划包括解释对应于减少乘积的范畴结构是什么。 显示英文摘要

摘要： Derived braids have been used to classify categorical structures based on the braid underlying a braided monoidal category V. With four-strand braids underlying the composition morphisms of tensor products of categories enriched over V, equality of derived braids has been seen to correspond with the results of Joyal and Street on coherence for braided monoidal categories, namely that diagrams commute when the braids underlying the legs of the diagram are equal. Equality of derived braids can then be seen as a generalization of the Yang-Baxter equation that appears in the work of Joyal and Street. The main result is a proof that decreasing products, which are braids formed from component braids with even numbers of strands, have equivalent derived braids. Plans for future work include interpreting what categorical structures correspond to decreasing products.