Geometry of a category of complexes and algebraic K-theory
The Grothendieck group of an abelian category A has a natural description in terms of the derived category of A, but it is wellknown that an analogous description of higher K-functors, even of \(K_ 1\), is not possible. In this paper the authors provide a new description of higher algebraic K-theory as the homotopy groups of a suitably defined classifying space for the category of bounded chain complexes in A. They construct this classifying space using a new notion of ''pseudo-functor'', and their main theorem asserts that the geometric realizations of six different constructions, among them Quillen's Q-construction and Waldhausen's S-construction, are homotopy equivalent. In an appendix, their methods are applied to classifying spaces of monoidal categories.
Grothendieck group of an abelian category
classifying spaces of monoidal categories
scientific article; zbMATH DE number 3917266