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.

References

For variations on the definition and some history, 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)

Revised on November 6, 2014 15:57:54
by David Corfield
(146.90.223.110)