Galois theory of simplicial complexes

AbstractWe examine basic notions of categorical Galois theory for the adjunction between Π0 and the inclusion as 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