On the algebraic characterization of the category of 3-dimensional cobordisms

Abstract

It is proved in \cite{BP} (arXiv:1108.2717) that the category of relative 3-dimensional cobordisms $\mathcal{C}o{b}^{2+1}$ is equivalent to the universal algebraic category $\overline{\overline{\mathcal{H}}}{}^r$ generated by a Hopf algebra object. A different algebraic category $\overline{\mathcal{A}lg}$ generated by a Hopf algebra object is defined in \cite{AS} and it conjectured to be equivalent to $\mathcal{C}o{b}^{2+1}$ as well. We prove that there exists a functor $\overline{\mathcal{A}lg}\to \overline{\overline{\mathcal{H}}}{}^r$, and use it to present an alternative set of axioms for $\overline{\overline{\mathcal{H}}}{}^r$.

arXiv comment21 pages, 21 figures