What is Mapping cone (topology)?

In mathematics, especially homotopy theory, the mapping cone is a construction C f {\displaystyle C_{f}} of topology, analogous to a quotient space. It is also called the homotopy cofiber, and also notated C f {\displaystyle Cf}. Its dual, a fibration, is called the mapping fibre. The mapping cone can be understood to be a mapping cylinder M f {\displaystyle Mf} , with one end of the cylinder collapsed to a point. Thus, mapping cones are frequently applied in the homotopy theory of pointed spaces.