  Generalizing the algebraic formulation of the First Fundamental Theorem of
Calculus (FFTC), a class of constraints involving a pair of operators was
considered in \cite{ZGK2}. For a given constraint, the existences of extensions
of differential and Rota-Baxter operators, of liftings of monads and comonads,
and of mixed distributive laws are shown to be equivalent. In this paper, we
give a classification of the constraints satisfying these equivalent
conditions.
