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String-net models for pivotal bicategories
Theory and applications of categories, Tome 44 (2025), pp. 474-543 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We develop a string-net construction of a modular functor whose algebraic input is a pivotal bicategory; this extends the standard construction based on a spherical fusion category. An essential ingredient in our construction is a graphical calculus for pivotal bicategories, which we express in terms of a category of colored corollas. The globalization of this calculus to oriented surfaces yields the bicategorical string-net spaces as colimits. We show that every rigid separable Frobenius functor between strictly pivotal bicategories induces linear maps between the corresponding bicategorical string-net spaces that are compatible with the mapping class group actions and with sewing. Our results are inspired by and have applications to the description of correlators in two-dimensional conformal field theories.
Publié le :
Classification : 18M20, 18N10, 57R56, 18M30
Keywords: String-net construction, pivotal bicategories, modular functors, Frobenius functors, graphical calculi 
@article{TAC_2025_44_a16,
     author = {J\"urgen Fuchs and Christoph Schweigert and Yang Yang},
     title = {String-net models for pivotal bicategories},
     journal = {Theory and applications of categories},
     pages = {474--543},
     year = {2025},
     volume = {44},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2025_44_a16/}
}
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Jürgen Fuchs; Christoph Schweigert; Yang Yang. String-net models for pivotal bicategories. Theory and applications of categories, Tome 44 (2025), pp. 474-543. http://geodesic.mathdoc.fr/item/TAC_2025_44_a16/