A right adjoint is a type of functor in category theory that associates to each object in one category a corresponding object in another category in a way that reflects a special relationship. This relationship is characterized by the existence of a natural transformation, which indicates how morphisms (arrows) between objects are preserved under the action of these functors. Right adjoints are significant because they often arise in various mathematical contexts, particularly in relation to limits, colimits, and preserving certain properties like exactness.
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