What is "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(C), which forms a spectrum. Let K(C) denote the loop space of the geometric realization ∣S(C)∣ of S(C). Then the group

πK(C) = π∣S(C)∣
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.