BASIC CONSTRUCTIONS IN THE K-THEORY OF HOMOTOPY RING SPACES

Abstract

Using the language of category theory and universal algebra we formalize the passage from the permutative category of finitely generated free R-modules to the algebraic K-theory KR of R and thus make it applicable to homotopy ring spaces. As applications we construct a Waldhausen type of algebraic K-theory for arbitrary homotopy ring spaces, show its equivalence with constructions of May and Steiner prove its Morita invariance and show that the algebraic K-theory KX of an E(infinity) ring X is itself an E(infinity) ring. Finally we investigate the monomial map Q(BX+*) --> KX.