Cofibration

In mathematics, in particular homotopy theory, a continuous mapping

i\colon 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. 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.

Basic theorems

 X \times I
to
 (A \times I) \cup (X \times \{0\}),

since this is the pushout and thus induces maps to every space sensible in the diagram.

Examples

References