at.algebraic topology - Definition for fundamental group (higher homotopy groups) for a category?

Quillen shows at the beginning of his article on higher algebraic K-theory that you can calculate the fundamental group $pi_1(C,a)$ of a category $C$ at an object $a$ by forming the localisation $C[Mor(C)^{-1}]$ at all arrows, then by taking $Hom(a,a) = Aut(a)$ in this groupoid. There are size issues, clearly, but for essentially small $C$ these can be ignored.