  Through careful analysis of an argument of Brooke-Taylor and Rosicky, we show
that the powerful image of any accessible functor is closed under colimits of
$\kappa$-chains, $\kappa$ a sufficiently large almost measurable cardinal. This
condition on powerful images, by methods resembling those of Lieberman and
Rosicky, implies $\kappa$-locality of Galois types. As this, in turn, implies
sufficient measurability of $\kappa$, via a paper of Boney and Unger, we obtain
an equivalence: a purely category-theoretic characterization of almost
measurable cardinals.
