论文标题
刚性编织类别的对称性
Symmetries of a rigid braided category
论文作者
论文摘要
我们确定每个刚性高辫子类别的自然对称性。具体而言，我们在每个$ \ nathcal {e} _ {n-1} $ - sonoidal $（g，d）$ - 类别$ \ mathcal $ \ mathcal {r} $上，每个对象是$ n \ geq 2 $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $， \ leq \ infty $）。此操作确定连续组$ω\ mathbb {r} \ mathbb {p}^{n-1} $在每个这样的$ \ mathcal {r} $上的模仿空间上的规范操作。如果参数$ n $，$ d $和$ g $很小，我们将这些连续的对称性与已知对称性进行比较，这些对称性表现为分类身份。
We identify natural symmetries of each rigid higher braided category. Specifically, we construct a functorial action by the continuous group $Ω\mathsf{O}(n)$ on each $\mathcal{E}_{n-1}$-monoidal $(g,d)$-category $\mathcal{R}$ in which each object is dualizable (for $n\geq 2$, $d \geq 0$, $d \leq g \leq \infty$). This action determines a canonical action by the continuous group $Ω\mathbb{R}\mathbb{P}^{n-1}$ on the moduli space of objects of each such $\mathcal{R}$. In cases where the parameters $n$, $d$, and $g$ are small, we compare these continuous symmetries to known symmetries, which manifest as categorical identities.
