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In this second part of a series work, we further develop the theory of higher fusion categories, including center functors, centralizers and group theoretic higher fusion categories. Along the way we prove several conjectures on modular extensions and the representation categories of finite higher groups.
We develop the mathematical theory of separable and unitary $n$-categories based on Gaiotto and Johnson-Freyds theory of condensation completion. We use it to study the categories of topological orders by including gapless quantum phases and defects.
It is shown that the endomorphism monoids of the category $2mathfrak{Cob}$ of all $2$-cobordisms do not have finitely axiomatizable equational theories. The same holds for the {topological annular category} and various quotients of the latter, like t
Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer - carryin
In this paper, which is subsequent to our previous paper [PS] (but can be read independently from it), we continue our study of the closed model structure on the category $mathrm{Cat}_{mathrm{dgwu}}(Bbbk)$ of small weakly unital dg categories (in the
Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation o