Waldhausen category

Summary

A Waldhausen category is a category with a zero object and two chosen classes of morphisms that satisfy a few axioms. These classes are the cofibrations and the weak equivalences. It is the input of Waldhausen's S-construction, which defines algebraic K-theory in this generality. Exact categories, categories of chain complexes with quasi-isomorphisms, and categories of spaces are all Waldhausen categories. This allows K-theory of rings, of schemes through perfect complexes, and of spaces to be treated in one framework.