#### Vol. 3, No. 2, 2009

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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 $R\otimes R$.

##### 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