On quasivarieties and varieties as categories

Studia Logica 78 (1-2):7 - 33 (2004)
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.
Keywords Philosophy   Logic   Mathematical Logic and Foundations   Computational Linguistics
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