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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.
@article{TAC_2001_8_a0, author = {Marino Gran and Maria Cristina Pedicchio}, title = {$n${-Permutable} locally finitely presentable categories}, journal = {Theory and applications of categories}, pages = {1--15}, publisher = {mathdoc}, volume = {8}, year = {2001}, language = {en}, url = {http://geodesic.mathdoc.fr/item/TAC_2001_8_a0/} }
Marino Gran; Maria Cristina Pedicchio. $n$-Permutable locally finitely presentable categories. Theory and applications of categories, Tome 8 (2001), pp. 1-15. http://geodesic.mathdoc.fr/item/TAC_2001_8_a0/