On multivarieties and multialgebraic categories

Multivarieties are classes of algebras presented by exclusive-or's of equat ions. A full characterization of categories which are equivalent to multiva rieties is presented, close to Lawvere's characterization of varieties. A c omparison with Diers' concept of multialgebraic category is presented: this is precisely a multivariety with effective equivalence relations. Besides, multialgebraic categories are shown to be precisely those categories which can be sketched by a (finite product, coproduct)-sketch. (C) 2001 Elsevier Science B.V. All rights reserved.