On the algebraic K-theory of model categories, by Steffen Sagave

In this short paper we prove a generalization of Waldhausen's Approximation Theorem which applies for example to categories with cofibrations and weak equivalences arising as subcategories of model categories. Using this, we show that an exact functor inducing an equivalence of homotopy categories also induces an equivalence in the algebraic K-theory. Furthermore, we state conditions on a model category under which the inclusion of the subcategory of finite cofibrant objects into the subcategory of homotopy finite cofibrant objects is a K-theory equivalence.

Steffen Sagave <sagave@math.uni-muenster.de>