Homological group completion theorem

Remark 5.5.4. Nikolaus also proves a homological group-completion theorem: after applying a multiplicative generalized homology theory, the map \(M\to \bOmega \bB M\) becomes algebraic localization under suitable Ore-type hypotheses. Its proof uses localization of ring spectra and their module categories. We will not develop that result in this book; the telescope criterion above is the part needed for complex K-theory.