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Characterization of protomodular varieties of universal algebras

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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.

http://www.tac.mta.ca/tac/volumes/11/6/11-06.dvi

http://www.tac.mta.ca/tac/volumes/11/6/11-06.ps

http://www.tac.mta.ca/tac/volumes/11/6/11-06.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/6/11-06.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/11/6/11-06.ps

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