A celebrated result in graph theory links the chromatic polynomial of a graph to the Tutte polynomial of the associated graphic matroid. In 2005, Helme-Guizon and Rong proved that the chromatic polynomial is categorified by a cohomological theory called chromatic cohomology. In this talk, I will describe how to associate a matroid to a directed graph G, called the multipath matroid of G, which encodes relevant combinatorial information about edge orientation. We also show that a specialization of the Tutte polynomial of the multipath matroid of G provides the number of certain "good" digraph colorings. Finally, analogously to the relationship between the chromatic polynomial and chromatic cohomology, I will show how the polynomial expressing the number of "good" digraph colorings is linked to multipath cohomology, introduced in a work with Caputi and Collari in 2021.