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

Primary: 16W30

Secondary: 18B40, 18D10

Authors