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Accessibility and the solution set condition. (English) Zbl 0817.18004

It was observed by M. Makkai and R. Paré [“Accessible categories”, Contemp. Math. 104 (1989; Zbl 0703.03042)] that given accessible categories \({\mathcal K}\) and \({\mathcal L}\), every accessible functor \(F : {\mathcal K} \to {\mathcal L}\) satisfies the solution-set condition. In the present paper the authors prove that, conversely, the solution-set condition guarantees that \(F\) is accessible. This result requires, in fact is equivalent to, the large cardinal Vopenka’s principle.
Reviewer: J.Adámek (Praha)

MSC:

18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18B15 Embedding theorems, universal categories

Citations:

Zbl 0703.03042
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References:

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