范畴自分配的上同调
Cohomology of Categorical Self-Distributivity
摘要：
我们在余代数和余交换余代数范畴中定义了自分配结构。我们得到的例子，从向量空间的基础是有限quandles的元素，一个李代数的直和与它的基域，和霍普夫代数。这些结构的自分配运算提供了杨-巴克斯特方程的解，反过来，杨-巴克斯特方程的解可以用来构造某些类别的自分配运算。此外，我们提出了一个上同调理论，包括李代数和quandle上同调，类似于Hochschild上同调，并可用于研究这些自分配结构的变形。这里的所有工作都是通过图表计算来通知的。
英文摘要：
We define self-distributive structures in the categories of coalgebras and cocommutative coalgebras. We obtain examples from vector spaces whose bases are the elements of finite quandles, the direct sum of a Lie algebra with its ground field, and Hopf algebras. The self-distributive operations of these structures provide solutions of the Yang--Baxter equation, and, conversely, solutions of the Yang--Baxter equation can be used to construct self-distributive operations in certain categories. Moreover, we present a cohomology theory that encompasses both Lie algebra and quandle cohomologies, is analogous to Hochschild cohomology, and can be used to study deformations of these self-distributive structures. All of the work here is informed via diagrammatic computations.
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