In mathematics, -equivalence, sometimes called right-left equivalence, is an equivalence relation between map germs. Let and be two manifolds, and let be two smooth map germs. We say that and are -equivalent if there exist diffeomorphism germs and such that In other words, two map germs are -equivalent if one can be taken onto the other by a diffeomorphic change of co-ordinates in the source (i.e. ) and the target (i.e. ).