Infinite loop space machine

In topology, a branch of mathematics, given a topological monoid X up to homotopy (in a nice way), an infinite loop space machine produces a group completion of X together with infinite loop space structure. For example, one can take X to be the classifying space of a symmetric monoidal category S; that is, [math]\displaystyle{ X = BS }[/math]. Then the machine produces the group completion [math]\displaystyle{ BS \to K(S) }[/math]. The space [math]\displaystyle{ K(S) }[/math] may be described by the K-theory spectrum of S.

References

• J. P. May and R. Thomason The uniqueness of infinite loop space machines