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Condensation inversion and Witt equivalence via generalised orbifolds

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Vincentas Mulevičius

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.

Keywords:
modular tensor categories, orbifold construction, topological quantum field theory

2020 MSC:
18M20,57K16

*Theory and Applications of Categories,*
Vol. 41, 2024,
No. 36, pp 1203-1292.

Published 2024-09-24.

http://www.tac.mta.ca/tac/volumes/41/36/41-36.pdf

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