Eckmann–Hilton duality

Summary

Eckmann–Hilton duality is a correspondence in homotopy theory between pairs of dual notions, obtained by reversing the direction of maps. Under it, the suspension corresponds to the loop space, cofibrations to fibrations, and the wedge sum to the product. It is a guiding principle, not a theorem: it suggests dual statements and dual proofs, but each dual statement must be checked on its own.