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The balanced tensor product of module categories

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arxiv 1406.4204 v3 pith:UMHUDBAY submitted 2014-06-17 math.QA math.CT

Christopher L. Douglas , Christopher Schommer-Pries , Noah Snyder This is my paper · ORCID
classification math.QAmath.CT
keywords productcategorybalancedtensorlinearbilinearcategoriescorepresenting
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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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Cited by 3 Pith papers

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    Explicit construction of dual bimodules from Frobenius algebras in monoidal 2-categories, with promotion of coherent duals and proof that special Frobenius algebras in 2Vect are rigid.

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