The McKay correspondence gives a bijection between finite subgroups of SU(2) and affine A,D,E Dynkin diagrams. There is a quantum version of this statement (due to Kirillov Jr and Ostrik) which relates "finite subgroups" of quantum sl(2) and finite A,D,E Dynkin diagrams. We use this correspondence to construct the category of "equivariant" coherent sheaves on the quantum projective line. This is done by defining analogues of the symmetric algebra and the structure sheaf, and using them to define a triangulated category which is a natural analogue of the derived category of equivariant sheaves on the projective line. We then produce natural objects in this triangulated category, and relate our category to the derived category of representations of the corresponding A,D,E quiver. This can be thought of as a quantum analogue of the projective McKay correspondence of Kirillov Jr. We will first review the classical constructions, then discuss the "quantum" analogues.