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European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
4
2013
4
A duality formalism in the spirit of Grothendieck and Verdier
Mitya
Boyarchenko
University of Michigan, ANN ARBOR, UNITED STATES
Vladimir
Drinfeld
University of Chicago, CHICAGO, UNITED STATES
Monoidal category, braided category, pivotal structure, ribbon category, $*$\nobreakdash-\hspace{0pt}autonomous category, Grothendieck–Verdier category
We study monoidal categories that enjoy a certain weakening of the rigidity property, namely, the existence of a dualizing object in the sense of Grothendieck and Verdier. We call them Grothendieck–Verdier categories. (They have also been studied in the literature under the name $*$-autonomous categories.) Notable examples include the derived category of constructible sheaves on a scheme (with respect to tensor product) as well as the derived and equivariant derived categories of constructible sheaves on an algebraic group (with respect to convolution). We show that the notions of pivotal category and ribbon category, which are well known in the setting of rigid monoidal categories, as well as certain standard results associated with these notions, have natural analogues in the world of Grothendieck–Verdier categories.
Category theory; homological algebra
General
447
489
10.4171/QT/45
http://www.ems-ph.org/doi/10.4171/QT/45