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

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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 
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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},
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     volume = {11},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2003_11_a5/}
}
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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/