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- W4320459512 abstract "In Muleviv{c}ius-Runkel, arXiv:2002.00663, it was shown how a so-called orbifold datum $mathbb{A}$ in a given modular fusion category (MFC) $mathcal{C}$ produces a new MFC $mathcal{C}_{mathbb{A}}$. Examples of these associated MFCs include condensations, i.e. the categories $mathcal{C}_B^circ$ of local modules of a separable commutative algebra $Binmathcal{C}$. In this paper we prove that the relation $mathcal{C} sim mathcal{C}_{mathbb{A}}$ on MFCs is the same as Witt equivalence. This is achieved in part by providing one with an explicit construction for inverting condensations, i.e. finding an orbifold datum $mathbb{A}$ in $mathcal{C}_B^circ$ whose associated MFC is equivalent to $mathcal{C}$. As a tool used in this construction we also explore what kinds of functors $Fcolonmathcal{C}rightarrowmathcal{D}$ between MFCs preserve orbifold data. It turns out that $F$ need not necessarily be strong monoidal, but rather a `ribbon Frobenius' functor, which has weak monoidal and weak comonoidal structures, related by a Frobenius-like property." @default.
- W4320459512 created "2023-02-14" @default.
- W4320459512 creator A5043217861 @default.
- W4320459512 date "2022-06-06" @default.
- W4320459512 modified "2023-09-26" @default.
- W4320459512 title "Condensation inversion and Witt equivalence via generalised orbifolds" @default.
- W4320459512 doi "https://doi.org/10.48550/arxiv.2206.02611" @default.
- W4320459512 hasPublicationYear "2022" @default.
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