论文标题
融合2类
Drinfeld Centers and Morita Equivalence Classes of Fusion 2-Categories
论文作者
论文摘要
我们证明，在莫里塔对等上，融合2类的德林菲尔德中心是不变的。我们继续表明，连接的融合2类别之间的莫里塔对等概念正好恢复了编织的融合1类别之间的等效概念。强烈的融合2类是一个融合2类，其编织的单型单位内态融合1类是$ \ mathbf {vect} $或$ \ mathbf {sVect} $。我们证明，每个Fusion 2类别都等同于强烈融合2类别和可逆融合2类别的2端子张量产品。我们继续表明，每个Fusion 2类都等同于连接的融合2类别。结果，我们发现融合2类中的每个刚性代数都是可分离的。这特别意味着每个融合2类都是可分开的。猜想的是，可分离性可确保融合2类是4偶化的。我们定义了Fusion 2类别的尺寸，并证明它始终是非零的。最后，我们证明了任何Fusion 2类别的Drinfeld中心都是有限的半神经2类别。
We prove that the Drinfeld center of a fusion 2-category is invariant under Morita equivalence. We go on to show that the concept of Morita equivalence between connected fusion 2-categories recovers exactly the notion of Witt equivalence between braided fusion 1-categories. A strongly fusion 2-category is a fusion 2-category whose braided fusion 1-category of endomorphisms of the monoidal unit is $\mathbf{Vect}$ or $\mathbf{SVect}$. We prove that every fusion 2-category is Morita equivalent to the 2-Deligne tensor product of a strongly fusion 2-category and an invertible fusion 2-category. We proceed to show that every fusion 2-category is Morita equivalent to a connected fusion 2-category. As a consequence, we find that every rigid algebra in a fusion 2-category is separable. This implies in particular that every fusion 2-category is separable. Conjecturally, separability ensures that a fusion 2-category is 4-dualizable. We define the dimension of a fusion 2-category, and prove that it is always non-zero. Finally, we show that the Drinfeld center of any fusion 2-category is a finite semisimple 2-category.
