Homotopy theory | Homotopical algebra
Cofibration
In mathematics, in particular homotopy theory, a continuous mapping , where and are topological spaces, is a cofibration if it lets homotopy classes of maps be extended to homotopy classes of maps whenever a map can be extended to a map where , hence their associated homotopy classes are equal . This type of structure can be encoded with the technical condition of having the homotopy extension property with respect to all spaces . This definition is dual to that of a fibration, which is required to satisfy the homotopy lifting property with respect to all spaces. This duality is informally referred to as Eckmann–Hilton duality. Because of the generality this technical condition is stated, it can be used in model categories. (Wikipedia).
