Characterization of protomodular varieties of universal algebras

Dominique Bourn and George Janelidze

Protomodular categories were introduced by the first author more than ten years ago. We show that a variety $\mathcal V$ 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 $i = 1, ..., n$.

Keywords: Maltsev and protomodular varieties, ideal determination

2000 MSC: 08B05,18C10; secondary: 08C05,18E10

Theory and Applications of Categories , Vol. 11, 2003, No. 6, pp 143-147.

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