In mathematics, specifically algebraic topology, the mapping cylinder of a continuous function f {\displaystyle f} between topological spaces X {\displaystyle X} and Y {\displaystyle Y} is the quotient M f = / ∼ {\displaystyle M_{f}=\,/\,\sim } where the ⨿ {\displaystyle \amalg } denotes the disjoint union, and ∼ is the equivalence relation generated by ∼ f for each x ∈ X. Wikipedia