Duality

A relationship that assigns to each object (and morphism) in one mathematical context a dual object (and dual morphism) in another or the same context, typically reversing direction of arrows or order and producing an involutive contravariant equivalence or correspondence. Duality often exchanges limits with colimits, substructures with quotient structures, or algebraic and geometric descriptions.

A contravariant correspondence between mathematical structures, often categories, that pairs objects and morphisms with dual counterparts by systematically reversing the direction of arrows while preserving key structural relations and properties.