A coherent dual of an object lifts to a coherent dual of a bimodule over Frobenius algebras; zigzag 2-isos need special Frobenius sections, and special Frobenius algebras in 2Vect are rigid.
The balanced tensor product of module categories
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The balanced tensor product M (x)_A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N. The balanced tensor product M [x]_C N of two module categories over a monoidal linear category C is the linear category corepresenting C-balanced right-exact bilinear functors out of the product category M x N. We show that the balanced tensor product can be realized as a category of bimodule objects in C, provided the monoidal linear category is finite and rigid.
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math.QA 2years
2026 2representative citing papers
Proposes axiomatic framework for derived skein modules of 3-manifolds that recovers ordinary skein modules in degree zero, with computable formulas, Hochschild formula for Sigma x S^1, first computations, and finiteness via deformation quantization.
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Frobenius Algebras and Dual Bimodules in Monoidal 2-Categories
A coherent dual of an object lifts to a coherent dual of a bimodule over Frobenius algebras; zigzag 2-isos need special Frobenius sections, and special Frobenius algebras in 2Vect are rigid.
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Derived skein module
Proposes axiomatic framework for derived skein modules of 3-manifolds that recovers ordinary skein modules in degree zero, with computable formulas, Hochschild formula for Sigma x S^1, first computations, and finiteness via deformation quantization.