Conditionally flat functors on spaces and groups

Emmanuel Dror Farjoun, Jérôme Scherer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Consider a fibration sequence F→E →B of topological spaces which is preserved as such by some functor L, so that LF→LE→LB is again a fibration sequence. Pull the fibration back along an arbitrary map X→B 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.

Original languageEnglish
Pages (from-to)149-160
Number of pages12
JournalCollectanea Mathematica
Volume66
Issue number1
DOIs
StatePublished - Jan 2014

Bibliographical note

Publisher Copyright:
© 2014, Universitat de Barcelona.

Keywords

  • Fiberwise localization
  • Flatness
  • Localization
  • Variety of groups

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