nLab
quasifibration

Contents

Definition

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

Revised on January 7, 2012 13:34:28 by Urs Schreiber (82.113.106.121)