K-theory of a bipermutative category
Special and general types
While a permutative category already induces a symmetric spectrum, representing the corresponding K-theory of a permutative category, for a bipermutative category this naturally carries the additional structure of an E-infinity ring spectrum. The generalized (Eilenberg-Steenrod) cohomology represented by this spectrum is called the (algebraic) K-theory of and it is hence a multiplicative cohomology theory.
Peter May, Ring Spaces and Ring spectra, Springer lectures notes in mathematics, Vol. 533, (1977) (pdf) chaper VI
Anthony Elmendorf, Michael Mandell, Rings, modules and algebras in infinite loop space theory, K-Theory 0680 (web, pdf)
Anthony Elmendorf, Michael Mandell, Permutative categories, multicategories, and algebraic K-theory (arXiv:0710.0082)
Revised on April 28, 2014 06:44:00
by Urs Schreiber