nLab
Serre fibration

Serre fibration $\Leftarrow$ Hurewicz fibration $\Rightarrow$ Dold fibration $\Leftarrow$ shrinkable map

Definition

A Serre fibration is a continuous map between topological spaces that has the right lifting property with respect to all inclusions of the form $i:{\Delta }^n\hookrightarrow {\Delta }^n\times I$ that include the standard topological $n$-simplex ${\Delta }^n\in$ Top as ${\Delta }^n\times \{0\}$.

This condition is a special case of that for a Hurewicz fibration.

The Serre fibrations serve as the abstract fibrations in the standard model structure on topological spaces.