Pseudomonads on monoidal bicategories

Some compatibility between monads and monoidal structures is needed for said structures to lift to the Eilenberg-Moore algebras, or to extend to the free algebras of the monad. We describe the appropriate analogous compatibility in the two-dimensional setting, now between pseudomonads and monoidal bicategories. We also treat braid, syllepsis and symmetry structures, and how these interact with pseudomonads. Potential applications include bicategorical models of linear and differential logic, and TQFT.