English

Fibrations up to an equivalence, homotopy colimits and pullbacks

Algebraic Topology 2010-01-14 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1001.2056,
  title  = {Fibrations up to an equivalence, homotopy colimits and pullbacks},
  author = {Lukáš Vokřínek},
  journal= {arXiv preprint arXiv:1001.2056},
  year   = {2010}
}
R2 v1 2026-06-21T14:33:59.044Z