Characterization of protomodular varieties of universal algebras
Dominique Bourn, George Janelidze · Theory and applications of categories · 2003
Protomodular categories were introduced by the first author more than ten years ago.We show that a variety V of universal algebras is protomodular if and only if it has 0-ary terms e 1 , . . ., e n , binary terms t 1 , . . ., t n , and (n+1)-ary term t satisfying the identities t(x, t 1 (x, y), . . ., t n (x, y)) = y and t i (x, x) = e i for each i = 1, . . ., n.