Geodesic
On the lattices of quasivarieties of differential groupoids
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 11-17

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The main result of Romanowska A., Roszkowska B., {\it On some groupoid modes\/}, Demonstratio Math. {\bf 20} (1987), no. 1--2, 277--290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is $\Cal Q$-universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties.
Classification : 08C15, 20N02
Keywords: mode; differential groupoid; lattice of subquasivarieties; $\Cal Q$-universal quasivariety 
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Kravchenko, A. V. On the lattices of quasivarieties of differential groupoids. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 11-17. http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a1/