  Adhesive categories provide an abstract framework for the algebraic approach
to rewriting theory, where many general results can be recast and uniformly
proved. However, checking that a model satisfies the adhesivity properties is
sometimes far from immediate. In this paper we present a new criterion giving a
sufficient condition for $\mathcal{M}, \mathcal{N}$-adhesivity, a
generalisation of the original notion of adhesivity. We apply it to several
existing categories, and in particular to hierarchical graphs, a formalism that
is notoriously difficult to fit in the mould of algebraic approaches to
rewriting and for which various alternative definitions float around.
