Weak Hopf monoids in braided monoidal categories

Pastro, Craig; Street, Ross

doi:10.2140/ant.2009.3.149

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Weak Hopf monoids in braided monoidal categories

Craig Pastro and Ross Street

Vol. 3 (2009), No. 2, 149–207

DOI: 10.2140/ant.2009.3.149

Abstract

We develop the theory of weak bimonoids in braided monoidal categories and show that they are in one-to-one correspondence with quantum categories with a separable Frobenius object-of-objects. Weak Hopf monoids are shown to be quantum groupoids. Each separable Frobenius monoid $R$ leads to a weak Hopf monoid $R \otimes R$ .

Keywords

weak bimonoids (weak bialgebra), weak Hopf monoids (weak Hopf algebra), quantum category, quantum groupoid, monoidal category

Mathematical Subject Classification 2000

Primary: 16W30

Secondary: 18B40, 18D10

Milestones

Received: 26 January 2008

Revised: 14 November 2008

Accepted: 23 December 2008

Published: 15 March 2009

Authors

Craig Pastro
Research Institute for the Mathematical Sciences Kyoto University Kyoto 606-8502 Japan
http://www.kurims.kyoto-u.ac.jp/~craig/
Ross Street
Department of Mathematics Macquarie University New South Wales 2109 Australia
http://www.maths.mq.edu.au/~street

Vol. 3, No. 2, 2009