Homotopy fiber
In mathematics, especially homotopy theory, the homotopy fiber (sometimes called the mapping fiber) is part of a construction that associates a fibration to an arbitrary continuous function of topological spaces . It acts as a homotopy theoretic kernel of a mapping of topological spaces due to the fact it yields a long exact sequence of homotopy groups
Moreover, the homotopy fiber can be found in other contexts, such as homological algebra, where the distinguished triangle
gives a long exact sequence analogous to the long exact sequence of homotopy groups. There is a dual construction called the homotopy cofiber.
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