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Susan Niefield - Monoidal (bi)categories, bimodules, and adjunctions
SUSAN NIEFIELD, Union College, Schenectady, New York 12308, USA | |
Monoidal (bi)categories, bimodules, and adjunctions |
In this joint work with Richard Wood, we consider variations of the following earlier result of the speaker. If is a monoidal category with coequalizers preserved by , then there is an adjoint pair
where takes a -monoid M to the category of M-M-bimodules and takes a monoidal functor to the -monoid pI.In each case, we consider a ``module'' functor which takes values in a category of monoidal categories with a suitable choice of morphisms. First, we replace by -cat and by monoidal categories over certain categories of matrices in . Next, we assume is symmetric and obtain an adjunction between commutative -monoids and monoidal -categories. Finally, we generalize this to an adjunction between braided monoidal -categories and monoidal -bicategories.
eo@camel.math.ca