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The balanced tensor product of module categories

Abstract:
The balanced tensor product M⊗AN of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M×N. The balanced tensor product M⊠CN 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×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.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1215/21562261-2018-0006

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Role:
Author
Publisher:
Duke University Press Publisher's website
Journal:
Kyoto Journal of Mathematics Journal website
Volume:
59
Issue:
1
Pages:
167-179
Publication date:
2018-10-03
Acceptance date:
2017-01-12
DOI:
EISSN:
2154-3321
ISSN:
2156-2261
Pubs id:
pubs:821734
URN:
uri:27ea85a8-eb9b-42a9-9009-58c6c9d9d646
UUID:
uuid:27ea85a8-eb9b-42a9-9009-58c6c9d9d646
Local pid:
pubs:821734

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