 when formula_3 is the unit interval formula_98, so that formula_99 can the thought of as either a homotopy of two functions from formula_4 to formula_57, or, equivalently, a single (continuous) path in formula_102.In algebraic topology, currying serves as an example of Eckmann–Hilton duality, and, as such, plays an important role in a variety of different settings.For example, loop space is adjoint to reduced suspensions; this is commonly written as
where formula_104 is the set of homotopy classes of maps formula_105, and formula_106 is the suspension of "A", and formula_107 is the loop space of "A".