Jonathan A. Barmak: Colorings of a poset, coverings and fundamental groups

A poset can be considered both as a category and a topological space. The latter being weak homotopy equivalent to its order complex. The categorical and the topological notions of covering coincide for posets. We study the coverings of a finite poset and its fundamental group through colorings of the Hasse diagram. These ideas are used to find presentations of the fundamental group. This is part of a joint work with Gabriel Minian.