Mapping Cone

- Mathematics & Logic -
Pure Mathematics Dictionary
The mapping cone Cf of a map f: X→Y is the quotient of the mapping cylinder Mf obtained by collapsing X×{0} to a point; equivalently Cf = Mf / (X×{0} ∼ *). The mapping cone models the homotopy cofiber of f and measures the failure of f to be surjective on homotopy.