quasifibration

**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**

**Introductions**

**Definitions**

**Paths and cylinders**

**Homotopy groups**

**Basic facts**

**Theorems**

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

- Tom Goodwillie, email to Don Davis and others, 16 May 2001 (txt)

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)

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