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.
Keywords: String-net construction, pivotal bicategories, modular functors, Frobenius functors, graphical calculi
2020 MSC: 18M20, 18N10, 57R56, 18M30
Theory and Applications of Categories, Vol. 44, 2025, No. 17, pp 474-543.
Published 2025-05-26.
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