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