Quandle Coloring Quivers

Given a finite quandle and subset of the quandle's endomorphism ring, we define a directed graph (also known as a quiver)-valued enhancement of the quandle counting invariant. Since quivers form small categories, this provides a categorification of the quandle counting invariant in the most literal sense. We use these quivers to define a new polynomial enhancement of the count invariant called the in-degree polynomial. This is joint work with Harvey Mudd College student Karina Cho.