We characterize $n$-permutable locally finitely presentable categories $Lex[{\mathcal C}^{op}, Set]$ by a condition on the dual of the essentially algebraic theory $\mathcal C^{op}$. We apply these results to exact Maltsev categories as well as to $n$-permutable quasivarieties and varieties.
Keywords: Locally finitely presentable categories, n-permutable and Maltsev varieties, quasivarieties.
2000 MSC: 18C05, 18C10, 18C35, 08C15.
Theory and Applications of Categories, Vol. 8, 2001, No. 1, pp 1-15.
http://www.tac.mta.ca/tac/volumes/8/n1/n1.dvi
http://www.tac.mta.ca/tac/volumes/8/n1/n1.ps
http://www.tac.mta.ca/tac/volumes/8/n1/n1.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n1/n1.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/8/n1/n1.ps