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, formula_1. Then the machine produces the group completion formula_2. The space formula_3 may be described by the K-theory spectrum of "S".