We show that the class of separable morphisms in the sense of G. Janelidze and W. Tholen in the case of Galois structure of second order coverings of simplicial sets due to R. Brown and G. Janelidze coincides with the class of covering maps of simplicial sets.
Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 169-173 http://jhrs.rmi.acnet.ge/volumes/2006/n1a6/