**Title**: Path Categories in A-Homotopy Theory

**Abstract**: A-homotopy theory is a discrete homotopy theory for graphs. While A-homotopy theory has many of the nice properties of the classical homotopy theory on topological spaces, we would like to know if it also has a nice structure to work with as well. We are pursuing this structure through path categories and homotopy type theory. In this talk, I will discuss why path categories might be the right option to get the structure that we are looking for in A-homotopy theory and how we can define a path category on the category of graphs (or something very close to it). This is joint work with Dr. Laura Scull.