Fibrations and nullifications
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The paper considers some aspects of the preservation of a fibrationF→E→B by a localization functorL, meaning thatLF→LE→LB is also a fibration. We obtain necessary and sufficient conditions for this, in caseL is equivalent to a nullification functorP 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.
KeywordsFundamental Group Homotopy Group Local Space Homology Theory Connected Space
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