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In Mulevičius-Runkel, Quant. Topol. 13:3 (2022), it was shown how a so-called orbifold datum A in a given modular fusion category (MFC) C produces a new MFC C(A). Examples of these associated MFCs include condensations, i.e. the categories of local modules of a separable commutative algebra B in C. In this paper we prove that the relation C~C(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 A in the category of local modules of B, whose associated MFC is equivalent to C. As a tool used in this construction we also explore what kinds of functors F:C->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.
@article{TAC_2024_41_a35,
author = {Vincentas Mulevi\v{c}ius},
title = {Condensation inversion and {Witt} equivalence via generalised orbifolds},
journal = {Theory and applications of categories},
pages = {1203--1292},
publisher = {mathdoc},
volume = {41},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a35/}
}
Vincentas Mulevičius. Condensation inversion and Witt equivalence via generalised orbifolds. Theory and applications of categories, Tome 41 (2024), pp. 1203-1292. http://geodesic.mathdoc.fr/item/TAC_2024_41_a35/