It is shown that accessibility of functors between accessible categories is fully characterized by Freyd's solution set condition, provided the set-theoretic Vopěnka principle holds. The Yoneda embedding of accessible categories satisfies the solution set condition; under Vopěnka's principle, this is true for all categories with a small dense generator. In each case, Vopěnka's principle is in fact equivalent to the validity of the desired results. © 1995.
Rosický, J., & Tholen, W. (1995). Accessibility and the solution set condition. Journal of Pure and Applied Algebra, 98(2), 189–208. https://doi.org/10.1016/0022-4049(94)00035-H