Galois theory of second order covering maps of simplicial sets Original Research Article

A classical theory gives an equivalence between the category of covering maps of a space and the category of actions on sets of the fundamental groupoid of the space. We give a corresponding theory in dimension 2 for simplicial sets as a consequence of a Generalised Galois Theory. This yields an equivalence between a category of 2-covering maps of a simplicial set B and a category of actions on groupoids of a certain double groupoid constructed from B.