标题： 图论的Yang-Baxter映射的结构范畴 显示英文标题

标题： Structure groupoids of quiver-theoretic Yang-Baxter maps

摘要： 与结构范畴和结构群胚相关的箭图理论量子Yang-Baxter方程的解。我们证明了可逆非退化解的结构群胚是Garside。这推广了Chouraqui关于集论解的结构群的一个著名结果。我们还从适当的呈现范畴中构造了可逆非退化解。然后我们研究了主齐次类型的解的情况。最后，我们给出了这个新类Garside群胚的一些例子。 显示英文摘要

摘要： Solutions to the quiver-theoretic quantum Yang-Baxter equation are associated with structure categories and structure groupoids. We prove that the structure groupoids of involutive non-degenerate solutions are Garside. This generalises a well-known result about the structure groups of set-theoretic solutions, due to Chouraqui. We also construct involutive non-degenerate solutions from suitable presented categories. We then investigate the case of solutions of principal homogeneous type. Finally, we present some examples of this new class of Garside groupoids.