K-theory spectrum

Summary

The K-theory spectrum of a ring, an exact category or a Waldhausen category is a spectrum whose homotopy groups are its algebraic K-groups. Its spaces are obtained by iterating Waldhausen's S-construction. Seeing K-theory as a spectrum makes the tools of stable homotopy theory available. Cofibre sequences give long exact sequences, and smashing with Moore spectra gives K-theory with finite coefficients. It is also the form in which K-theory is compared with other cohomology theories.