Eilenberg-Moore Bicategories for Opmonoidal Pseudomonads

We analyse compatibility between monads and monoidal structures in the two-dimensional setting. We describe sufficient conditions for monoidal structures to lift to the Eilenberg-Moore pseudoalgebras. We then extend these results to braids, syllapses and symmetries. To achieve these results we define the $\mathbf{Gray}$-tensor product of pseudomonads, and examine its interaction with the Eilenberg-Moore construction.