Geodesic
On flat covers in varieties
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 19-24.

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Flat covers do not exist in all varieties. We give a necessary condition for the existence of flat covers and some examples of varieties where not all algebras have flat covers.
Classification : 16D40, 18G05, 18G30
Keywords: flat object; flat cover; variety; cosimplicial object 
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Kruml, David. On flat covers in varieties. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 19-24. http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a2/