Abstract
Finitary quasivarieties are characterized categorically by the existence of colimits and of an abstractly finite, regularly projective regular generator G. Analogously, infinitary quasivarieties are characterized: one drops the assumption that G be abstractly finite. For (finitary) varieties the characterization is similar: the regular generator is assumed to be exactly projective, i.e., hom(G, −) is an exact functor. These results sharpen the classical characterization theorems of Lawvere, Isbell and other authors.
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Supported by the Czech Grant Agency (Project 201/02/0148).
Special issue of Studia Logica: “Algebraic Theory of Quasivarieties” Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko
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Adámek, J. On quasivarieties and varieties as categories. Stud Logica 78, 7–33 (2004). https://doi.org/10.1007/s11225-005-7033-6
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DOI: https://doi.org/10.1007/s11225-005-7033-6