A cofibration is a map with the homotopy extension property. An inclusion of a CW complex into another as a subcomplex is a cofibration; collapsing that subcomplex gives the quotient used in the K-theory six-term exact sequence.
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In topology, a cofibration is a specific type of map between topological spaces that satisfies certain conditions. Cofibrations play a crucial role in homotopy theory and the study of fibration and cofibration sequences. They are often defined in terms of the homotopy extension property. ### Definition: A map \( i : A \to X \) is called a **cofibration** if it satisfies the homotopy extension property with respect to any space \( Y \).