S construction

In mathematics, specifically in algebraic K-theory, the Waldhausen S-construction produces from a Waldhausen category C a sequence of Kan complexes S n ( C ) , which forms a spectrum. Let K ( C ) denote the loop space of the geometric realization | S ∗ ( C ) | of S ∗ ( C ) . Then the group

is the n-th K-group of C. Thus, it gives a way to define higher K-groups. Another approach for higher K-theory is Quillen's Q-construction.

The construction is due to Friedhelm Waldhausen.