the abstract I sent to "categories" lost a few sentences... Best regards Marco ___ The following preprint is available: M. Grandis - G. Janelidze Galois theory of simplicial complexes Dip. Mat. Univ. Genova, Preprint 459 (2002), 9 p. Abstract We examine basic notions of categorical Galois theory for the adjunction (\Pi_0 -| discrete) in the case of simplicial complexes. Covering morphisms are characterized as the morphisms satisfying the unique simplex lifting property and are classified by means of the fundamental groupoid, for which we give an explicit "Galois-theoretic" description. The class of covering morphisms is a part of a factorization system similar to the (purely inseparable, separable) factorization system in classical Galois theory, which however fails to be the (monotone, light) factorization. http://www.dima.unige.it/~grandis/rec.public_grandis.html ftp://www.dima.unige.it/Home/grandis/public/GalSmc.pdf With best regards Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ ftp://www.dima.unige.it/Home/grandis/public/ 16-Sep-2002 11:47:46 -0300,4471;000000000001-00000000