The notion of a fibration generalizes the notion of a fiber bundle and plays an important role in algebraic topology, a branch of mathematics.

Fibrations are used, for example, in Postnikov systems or obstruction theory.

In this article, all mappings are continuous mappings between topological spaces.

A mapping ${\displaystyle p\colon E\to B}$ satisfies the homotopy lifting property for a space ${\displaystyle X}$ if:

there exists a (not necessarily unique) homotopy ${\displaystyle {\tilde {h}}\colon X\times [0,1]\to E}$ lifting ${\displaystyle h}$ (i.e. ${\displaystyle h=p\circ {\tilde {h}}}$) with ${\displaystyle {\tilde {h}}_{0}={\tilde {h}}|_{X\times 0}.}$

The following commutative diagram shows the situation:

A fibration (also called Hurewicz fibration) is a mapping ${\displaystyle p\colon E\to B}$ satisfying the homotopy lifting property for all spaces ${\displaystyle X.}$ The space ${\displaystyle B}$ is called base space and the space ${\displaystyle E}$ is called total space. The fiber over ${\displaystyle b\in B}$ is the subspace ${\displaystyle F_{b}=p^{-1}(b)\subseteq E.}$

A Serre fibration (also called weak fibration) is a mapping ${\displaystyle p\colon E\to B}$ satisfying the homotopy lifting property for all CW-complexes.