Vol. 3, No. 2, 2009

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Weak Hopf monoids in braided monoidal categories

Craig Pastro and Ross Street

Vol. 3 (2009), No. 2, 149–207
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 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