Farjoun, Emmanuel Dror
Scherer, Jerome
Conditionally flat functors on spaces and groups
Collectanea Mathematica
0010-0757
10.1007/s13348-013-0102-7
66
1
149-160
12
Consider a fibration sequence of topological spaces which is preserved as such by some functor , so that is again a fibration sequence. Pull the fibration back along an arbitrary map into the base space. Does the pullback fibration enjoy the same property? For most functors this is not to be expected, and we concentrate mostly on homotopical localization functors. We prove that the only homotopical localization functors which behave well under pull-backs are nullifications. The same question makes sense in other categories. We are interested in groups and how localization functors behave with respect to group extensions. We prove that group theoretical nullification functors behave nicely, and so do all epireflections arising from a variety of groups.
Localization;
Flatness;
Fiberwise localization;
Variety of groups;
Springer-Verlag Italia Srl
Milan
2015