What is "cofibration"

n. (context mathematics English) A particular form of mapping. A continuous mapping $icolon\; A\; to\; X$, where ''A'' and ''X'' are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to all spaces ''Y''.

In mathematics, in particular homotopy theory, a continuous mapping

i: A → X
,

where A and X are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to all spaces Y. The name is because the dual condition, the homotopy lifting property, defines fibrations. For a more general notion of cofibration see the article about model categories.