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

\pi_n K(C) = \pi_{n+1} |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.

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