in order to fully develop "a"-theory, waldhausen made significant technical advances in the foundations of "k"-theory. waldhausen introduced waldhausen categories, and for a waldhausen category "c" he introduced a simplicial category "s""c" (the "s" is for segal) defined in terms of chains of cofibrations in "c". this freed the foundations of "k"-theory from the need to invoke analogs of exact sequences.