Fibrewise nullification and the cube theorem
David Chataur and Jerome Scherer
CRM Barcelona, dchataur@crm.es
Universidad Autonoma de Barcelona, jscherer@mat.uab.es
Our aim is to construct fibrewise localizations in model categories.
For pointed spaces, the general idea is to decompose the total space
of a fibration as a diagram over the category of simplices of the base
and replace it by the localized diagram. This of course is not possible
in an arbitrary category. We have thus to adapt another construction
which heavily depends on Mather's cube theorem. Working with model
categories in which the cube theorem holds, we characterize
completely those who admit a fibrewise nullification. As an
application we get fibrewise plus-construction and fibrewise
Postnikov sections for algebras over an operad.