-Cat is locally presentable or locally bounded if is so.
Kelly, G.M., Lack, Stephen (2001)
Theory and Applications of Categories [electronic only]
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Kelly, G.M., Lack, Stephen (2001)
Theory and Applications of Categories [electronic only]
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Borceux, F., Quinteiro, C., Rosický, J. (1998)
Theory and Applications of Categories [electronic only]
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Jiří Adámek, Jiří Rosický (1989)
Archivum Mathematicum
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G. M. Kelly (1982)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Jiří Adámek, Jiří Rosický (1996)
Commentationes Mathematicae Universitatis Carolinae
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For categories with equalizers the concepts ``accessible'' and ``axiomatizable'' are equivalent. This results is proved under (in fact, is equivalent to) the large-cardinal Vopěnka's principle.
G. M. Kelly (1986)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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