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research article

Conditionally flat functors on spaces and groups

Farjoun, Emmanuel Dror
•
Scherer, Jerome
2015
Collectanea Mathematica

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.

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Type
research article
DOI
10.1007/s13348-013-0102-7
Web of Science ID

WOS:000347246500008

Author(s)
Farjoun, Emmanuel Dror
Scherer, Jerome
Date Issued

2015

Publisher

Springer-Verlag Italia Srl

Published in
Collectanea Mathematica
Volume

66

Issue

1

Start page

149

End page

160

Subjects

Localization

•

Flatness

•

Fiberwise localization

•

Variety of groups

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
UPHESS  
Available on Infoscience
February 20, 2015
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/111336
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