  Given a 2-category $\twocat{K}$ admitting a calculus of bimodules, and a
2-monad T on it compatible with such calculus, we construct a 2-category
$\twocat{L}$ with a 2-monad S on it such that: (1)S has the
adjoint-pseudo-algebra property. (2)The 2-categories of pseudo-algebras of S
and T are equivalent. Thus, coherent structures (pseudo-T-algebras) are
transformed into universally characterised ones (adjoint-pseudo-S-algebras).
The 2-category $\twocat{L}$ consists of lax algebras for the pseudo-monad
induced by T on the bicategory of bimodules of $\twocat{K}$. We give an
intrinsic characterisation of pseudo-S-algebras in terms of representability.
Two major consequences of the above transformation are the classifications of
lax and strong morphisms, with the attendant coherence result for
pseudo-algebras. We apply the theory in the context of internal categories and
examine monoidal and monoidal globular categories (including their monoid
classifiers) as well as pseudo-functors into $\Cat$.
