A category-theoretic characterization of almost measurable cardinals

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... Show more