In mathematics a Waldhausen category (after Friedhelm Waldhausen) is a category C with a zero object equipped with cofibrations co(C) and weak equivalences we(C), both containing all isomorphisms, both compatible with pushout, and co(C) containing the unique morphisms from the zero-object to any object A. To be more precise about the pushouts, we require when is a cofibration and is any map, that we have a push-out where the map is a cofibration: File:Waldhausen cat.png for which of bounded chaincomplexes on an exact category The category of functors when is so.And given a diagram , then is.