The balanced tensor product of module categories

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.

19 pages; v3 is author-final version

References in corpus (4)

• Bicategories for boundary conditions and for surface defects in 3-d TFT
• Integrating quantum groups over surfaces
• (Op)lax natural transformations, twisted quantum field theories, and "even higher" Morita categories
• Quantum subgroups of the Haagerup fusion categories

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• The 2-Deligne Tensor Product
• Compact Semisimple 2-Categories
• Local Modules in Braided Monoidal 2-Categories
• Constructing non-semisimple modular categories with local modules
• Gauging Defects in Quantum Spin Systems
• Davydov-Yetter cohomology and relative homological algebra
• The Symmetry Enriched Center Functor is Fully Faithful
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• Commutative algebras in Grothendieck-Verdier categories, rigidity, and vertex operator algebras
• Analytic Conformal Blocks of $C_2$-cofinite Vertex Operator Algebras III: The Sewing-Factorization Theorems