Fibrations up to an equivalence, homotopy colimits and pullbacks

Details Fibrations up to an equivalence, homotopy colimits and pullbacks Fibrations up to an equivalence, homotopy colimits and pullbacks

2010-01-13

arxiv.org/abs/1001.2056v1

Mathematics

Algebraic Topology

Scientific paper

We gather conditions on a class H of continuous maps of topological spaces that allow a reasonable theory of fibrations up to an equivalence (a map from this class) which we call H-fibrations. The weak homotopy equivalences recover quasifibrations and homology equivalences yield homology fibrations. We study local H-fibrations that behave nicely with respect to homotopy colimits together with universal H-fibrations that behave nicely with respect to pullbacks. We then proceed to classify H-fibrations up to a natural notion of equivalence.

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