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Szlach\'anyi showed that bialgebroids can be characterised using skewmonoidal categories. The characterisation reduces the amount of data,structure, and properties required to define them. Lack and Street provide abicategorical account of that same fact; they characterise quantum categoriesin terms of skew monoidal structures internal to a monoidal bicategory. Aquantum category is an opmonoidal monad on an enveloping monoidale$R^\circ\otimes R$ in a monoidal bicategory. In a previous paper, wecharacterised opmonoidal arrows on enveloping monoidales as a simpler structurecalled oplax action.  This is the second paper based on the author's PhD thesis. Here, motivated bythe fact that opmonoidal monads are monads in the bicategory of monoidales,opmonoidal arrows, and opmonoidal cells; we prove that right skew monoidalesare "monads of oplax actions". To do so, we arrange oplax actions as the1-simplices of a simplicial object in $\mathsf{Cat}$. In nice cases thissimplicial object is ought to be thought as a bicategory whose arrows are oplaxactions, that is to say, it is weakly equivalent to a nerve of a bicategory. Wedefine monads of oplax actions as simplicial maps out of the Catalan simplicialset and prove that these are in bijective correspondence with right skewmonoidales whose unit has a right adjoint, no assumptions required on theambient monoidal bicategory.

Monads of oplax actions are skew monoidales