Conditionally flat functors on spaces and groups

Autores: Emmanuel Dror Farjoun , Jérôme Scherer
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 1, 2015, págs. 149-160
Idioma: inglés
DOI: 10.1007/s13348-013-0102-7
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Resumen
- 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.