In the spring of 1972, Quillen found another approach to the construction of higher "K"-theory which was to prove enormously successful. This new definition began with an exact category, a category satisfying certain formal properties similar to, but slightly weaker than, the properties satisfied by a category of modules or vector bundles. From this he constructed an auxiliary category using a new device called his ""Q"-construction." Like Segal's Γ-objects, the "Q"-construction has its roots in Grothendieck's definition of "K"0. Unlike Grothendieck's definition, however, the "Q"-construction builds a category, not an abelian group, and unlike Segal's Γ-objects, the "Q"-construction works directly with short exact sequences. If "C" is an abelian category, then "QC" is a category with the same objects as "C" but whose morphisms are defined in terms of short exact sequences in "C". The "K"-groups of the exact category are the homotopy groups of Ω"BQC", the loop space of the geometric realization (taking the loop space corrects the indexing). Quillen additionally proved his " theorem" that his two definitions of "K"-theory agreed with each other. This yielded the correct "K"0 and led to simpler proofs, but still did not yield any negative "K"-groups.