nLab quasifibration



Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology



Paths and cylinders

Homotopy groups

Basic facts




A quasifibration is a kind of fibration, a morphism in homotopy theory that acts like a fibration in that the actual fibres are, via the canonical inclusions, weakly homotopy equivalent to the homotopy fibres (note that no lifting properties are used in the definition). As a result the long exact sequence in homotopy for the replacement of the map by a fibration becomes an long exact sequence for the map itself.


For variations on the definition and some history, see

Also see

  • Peter May, Weak Equivalences and Quasifibrations, in: Groups of Self-Equivalences and Related Topics, Lecture Notes in Mathematics Volume 1425, 1990, pp 91-101 (pdf, doi: 10.1007/BFb0083834)

Last revised on February 15, 2019 at 14:53:33. See the history of this page for a list of all contributions to it.