Given a class of morphisms in a closed model category one can consider
the corresponding class of local objects and the morphisms which
define bijections on the Hom-sets with values in local objects form
the "left Bousfield closure" of the original class. In the additive
context (e.g. for triangulated categories) there is a complimentary
approach to the problem of "saturating" a given class of morphisms
based on the concept of a thick subcategory which leads to the same
result if everything is compactly generated. The goal of this paper is
to develop an analog of the second approach to saturation in the non
additive context.
This paper has been supplanted by Simplicial radditive functors.