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In category theory, a branch of mathematics, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation, and (dually) cogenerators are objects which envelope other objects as an approximation.
More precisely:
- A generator of a category with a zero object is an object G such that for every nonzero object H there exists a nonzero morphism f: G → H.
- A cogenerator is an object C such that for every nonzero object H there exists a nonzero morphism f: H → C. (Note the reversed order).