发表机构
Université de Montpellier（蒙彼利埃大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了一个三维ETQFT，统一了Kerler-Lyubashenko TQFT及其修正迹版本，并去掉容许性条件，使其圆范畴等价于原模范畴。
AI 中文摘要
本文旨在阐明与（未必半单的）模范畴 $\mathcal{C}$ 的伴随端 $\mathcal{E}$ 相关联的 Kerler-Lyubashenko TQFT $J_\mathcal{E}$ 与其基于 $\mathcal{C}$ 的投射对象理想 $\mathrm{Proj}(\mathcal{C})$ 所支持的修正迹的规范化版本 $V_\mathcal{E}$ 之间的关系。更确切地说，我们构造了一个三维 ETQFT $\boldsymbol{\hat{A}}_\mathcal{E}$，它同时包含 $J_\mathcal{E}$ 和 $V_\mathcal{E}$。ETQFT $\boldsymbol{\hat{A}}_\mathcal{E}$ 由一个 $2$-函子给出，其源范畴是容许的三维配边 $2$-范畴，其目标范畴是有限完备的线性范畴 $2$-范畴。我们通过去掉曲面的容许性条件改进了该构造的早期版本。由此，我们得到一个 ETQFT，其圆范畴 $\boldsymbol{\hat{A}}_\mathcal{E}(\boldsymbol{S}^1)$ 等价于范畴 $\mathcal{C}$，而非理想 $\mathrm{Proj}(\mathcal{C})$。
英文摘要
The goal of this paper is to clarify the relation between the Kerler-Lyubashenko TQFT $J_\mathcal{E}$ associated with the adjoint end $\mathcal{E}$ of a (not necessarily semisimple) modular category $\mathcal{C}$ and its renormalized version $V_\mathcal{E}$ based on the modified trace supported by the ideal $\mathrm{Proj}(\mathcal{C})$ of projective objects of $\mathcal{C}$. More precisely, we construct a $3$-dimensional ETQFT $\boldsymbol{\hat{A}}_\mathcal{E}$ that contains both $J_\mathcal{E}$ and $V_\mathcal{E}$. The ETQFT $\boldsymbol{\hat{A}}_\mathcal{E}$ is given by a $2$-functor whose source is the $2$-category of admissible $3$-dimensional cobordisms, and whose target is the $2$-category of finitely complete linear categories. We improve on earlier versions of the construction by dropping the admissibility condition for surfaces. By doing so, we obtain an ETQFT whose circle category $\boldsymbol{\hat{A}}_\mathcal{E}(\boldsymbol{S}^1)$ is equivalent to the category $\mathcal{C}$, as opposed to the ideal $\mathrm{Proj}(\mathcal{C})$.
Comments77 pages
