×

Separable morphisms of simplicial sets. (English) Zbl 1132.55009

The paper describes the class of separable morphisms for a Galois structure [cf. R. Brown and G. Janelidze, J. Pure Appl. Algebra 135, No. 1, 23–31 (1999; Zbl 0930.55009)]. This one, together with an adjunction of functors, considers classes of morphisms called fibrations. Separable morphisms are particular fibrations. The main result states that separable morphisms arc exactly the Kan fibrations which are covering maps of simplicial sets.

MSC:

55U10 Simplicial sets and complexes in algebraic topology
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18G55 Nonabelian homotopical algebra (MSC2010)
57M10 Covering spaces and low-dimensional topology

Citations:

Zbl 0930.55009
PDFBibTeX XMLCite
Full Text: arXiv EuDML EMIS