where formula_105 is the set of homotopy classes of maps formula_106, and formula_107 is the suspension of "A", and formula_108 is the loop space of "A". In essence, the suspension formula_109 can be seen as the cartesian product of formula_3 with the unit interval, modulo an equivalence relation to turn the interval into a loop. The curried form then maps the space formula_3 to the space of functions from loops into formula_58, that is, from formula_3 into formula_114. Then formula_85 is the adjoint functor that maps suspensions to loop spaces, and uncurrying is the dual.