Geodesic
Characterization of protomodular varieties of universal algebras
Theory and applications of categories, Tome 11 (2003), pp. 143-147

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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 $i = 1, ..., n$.

Classification : 08B05, 18C10, secondary: 08C05, 18E10
Keywords: Maltsev and protomodular varieties, ideal determination 
Dominique Bourn; George Janelidze. Characterization of protomodular varieties of universal algebras. Theory and applications of categories, Tome 11 (2003), pp. 143-147. http://geodesic.mathdoc.fr/item/TAC_2003_11_a5/
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     author = {Dominique Bourn and George Janelidze},
     title = {Characterization of protomodular varieties of universal algebras},
     journal = {Theory and applications of categories},
     pages = {143--147},
     year = {2003},
     volume = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2003_11_a5/}
}
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