Injective Cogenerator

See also cogenerator

In category theory, 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. When working with unfamiliar algebraic objects, one can use these to approximate with the more familiar.

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).