A mirror homotopy is the evolution of a given structure into a "mirror structure": a structure of the same type related to the former by a natural symmetry (mirror) of a fixed invariant. In music theory, an example of of a mirror pair is given by a quantum melodic and its semi-classical limit. In this case, the mirror homotopy is given by letting the Planck constant tend to zero. Since invariants change, mirror deformations are not continuous, and are usually parametrized by disconnected spaces such as Cantor sets.
Mirror
Homotopy