Rosický, Jiří A categorical characterization of sets among classes. (English) Zbl 0632.18003 Arch. Math., Brno 23, 117-119 (1987). The author considers the classes X for which \(2^ X\) exists (small classes) and proves that X is a set if and only if any X-indexed union of small classes is small. One can notice that the existence of small classes which are not sets is considered only in the absence of the axiom of regularity. Reviewer: I.Tofan MSC: 18B05 Categories of sets, characterizations 03E65 Other set-theoretic hypotheses and axioms Keywords:power object; small classes; set; axiom of regularity × Cite Format Result Cite Review PDF Full Text: EuDML