The loop space of the $Q$-construction

Abstract

The higher algebraic K-groups are defined as gi.//[ 'lri+ lQ'I rl Q'I for an exact category J/. We present a simplicial set Gt' with the property that a'l is naturally homotopy equivalent to the loop space IQ'I, and thus Kilt' %1G'I. In this way we given an algebraic description of the loop space, which a priori, has no such description.