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A functor acts faithfully on the right of a class of objects of if it distinguishes morphisms out of objects of (that is, and implies . We define a full subcategory such that acts faithfully on the right of the objects of . An object is a generator if is faithful, and if is not faithful, we may still consider . This gives rise to the notion of a generating structure. Cogenerating structures are defined dually, and various canonical generating and cogenerating structures are defined for the category of -modules. Relationships between these can be used in the homological classification of rings. References