  In a previous paper I gave a presentation for the Quillen higher algebraic
K-groups of an exact category in terms of "acyclic binary multicomplexes". In
this paper I take that presentation as a definition of the higher K-groups,
generalize it to the relative K-groups of an exact functor between exact
categories, and produce the corresponding long exact sequence by elementary
means, without homotopy theory.

K-Theory and Homology