Suppose f & g are both functions mapping from A to B. (A & B are topological spaces.)
Also assume that f & g are homotopic.
Then how does one prove that the Mapping Cylinders of f & g are homotopic spaces?
Is it THAT simple? Y is a deformation retract of both Mf & Mg, so Y is homotopic to Mf & Mg & therefore, as homotopy is an equivalence relation, Mf is homotopic to Mg?
Are you sure there's nothing else to it? I spent aaaaaaaaaaaaages playing around with homtopies like F:Mfx[0,1] ---> Mg, etc. Do you not need to do ANY of that?? x