On the algebraic \(K\)-theory of infinite product categories
It is shown that the \(K\)-theory functor in the category of symmetric monoidal categories preserves arbitrary products. For finite products, this is an easy observation, but for infinite products one has to work. The work takes place in a simplicial setting and uses Waldhausen's definition of \(K\)-theory in terms of categories with cofibrations, weak equivalences and cylinder functors. It is shown that \(K\)-theory spectra obtained this way are close enough to being Kan for the desired conclusion (which would be easy if all complexes were Kan) to be available.
scientific article; zbMATH DE number 800394