On Categories of Algebras Equivalent to a Quasivariety
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In a recent paper, B. Banaschewski proved that anySP-class of algebras which is category equivalent to a variety (over a possibly different finitary similarity type) is itself a variety. Here we prove the analogous statement obtained by replacing “variety” with “quasivariety”. We also present examples which detail some of the difficulties arising when one tries to strengthen the theorem in various ways.
Bankston, Paul and Fox, Ralph, "On Categories of Algebras Equivalent to a Quasivariety" (1983). Mathematics, Statistics and Computer Science Faculty Research and Publications. 170.