论文标题
关于三维恢复类别的代数表征
On the algebraic characterization of the category of 3-dimensional cobordisms
论文作者
论文摘要
在\ cite {bp}（arxiv：1108.2717）中证明了相对3维共同体的类别$ \ cal cob^{2+1} $等效于宇宙代数类别$ \ edline $ \ edline {\ cal h h anbr at {\ cal albra abla，a n a a a i nline {\ cal albra a in a i gentra。在\ cite {as}中定义了另一个代数类别$ \ overline {\ cal alg} $，也定义了它的指出等同于$ \ cal cob^{2+1} $。我们证明存在一个函数$ \叠加{\ cal alg} \ to \ overline {\ overline {\ cal h}} {} {}^r $，并使用它来展示$ \ edline {\ edline {\ edline {\ cal h h}}}的替代公理集。
It is proved in \cite{BP} (arXiv:1108.2717) that the category of relative 3-dimensional cobordisms $\cal Cob^{2+1}$ is equivalent to the universal algebraic category $\overline{\overline{\cal H}}{}^r$ generated by a Hopf algebra object. A different algebraic category $\overline{\cal Alg}$ generated by a Hopf algebra object is defined in \cite{AS} and it conjectured to be equivalent to $\cal Cob^{2+1}$ as well. We prove that there exists a functor $\overline{\cal Alg}\to \overline{\overline{\cal H}}{}^r$, and use it to present an alternative set of axioms for $\overline{\overline{\cal H}}{}^r$.
