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.
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