  We develop a theory of covering digraphs, similar to the theory of covering
spaces. By applying this theory to Cayley digraphs, we build a "bridge" between
GLMY-theory and group homology theory, which helps to reduce path homology
calculations to group homology computations. We show some cases where this
approach allows us to fully express path homology in terms of group homology.
To illustrate this method, we provide a path homology computation for the
Cayley digraph of the additive group of rational numbers with a generating set
consisting of inverses to factorials. The main tool in our work is a filtered
simplicial set associated with a digraph, which we call the filtered nerve of a
digraph.
