Fibrations and nullifications

A. J. Berrick; E. Dror Farjoun

doi:10.1007/BF02776058

Fibrations and nullifications

A. J. Berrick^*, E. Dror Farjoun

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The paper considers some aspects of the preservation of a fibration F → E → B by a localization functor L, meaning that LF → LE → LB is also a fibration. We obtain necessary and sufficient conditions for this, in case L is equivalent to a nullification functor P_w. Applications include the fact that if such a fibration is preserved by a nullification, then so too are all of its pullbacks. Another application is a homological criterion for a fibration to be preserved. No similar results are known for general localization functors.

Original language	English
Pages (from-to)	205-220
Number of pages	16
Journal	Israel Journal of Mathematics
Volume	135
DOIs	https://doi.org/10.1007/BF02776058
State	Published - 2003

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abstract = "The paper considers some aspects of the preservation of a fibration F → E → B by a localization functor L, meaning that LF → LE → LB is also a fibration. We obtain necessary and sufficient conditions for this, in case L is equivalent to a nullification functor Pw. Applications include the fact that if such a fibration is preserved by a nullification, then so too are all of its pullbacks. Another application is a homological criterion for a fibration to be preserved. No similar results are known for general localization functors.",

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AB - The paper considers some aspects of the preservation of a fibration F → E → B by a localization functor L, meaning that LF → LE → LB is also a fibration. We obtain necessary and sufficient conditions for this, in case L is equivalent to a nullification functor Pw. Applications include the fact that if such a fibration is preserved by a nullification, then so too are all of its pullbacks. Another application is a homological criterion for a fibration to be preserved. No similar results are known for general localization functors.

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Fibrations and nullifications

Abstract

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