Algebra & Number Theory

Weak Hopf monoids in braided monoidal categories

Craig Pastro and Ross Street

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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 RR.

Article information

Algebra Number Theory, Volume 3, Number 2 (2009), 149-207.

Received: 26 January 2008
Revised: 14 November 2008
Accepted: 23 December 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16W30
Secondary: 18B40: Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx] 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]

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


Pastro, Craig; Street, Ross. Weak Hopf monoids in braided monoidal categories. Algebra Number Theory 3 (2009), no. 2, 149--207. doi:10.2140/ant.2009.3.149.

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