The dual notion of a projective object is that of an injective object. An object in an abelian category
if the
functor from
to
is exact.
Examples. Let be a ring with 1. Consider the category of left -modules
.
is an abelian category. The projective objects in
are precisely the projective left -modules. So is itself a projective object in
. Dually, the injective objects in
are exactly the injective left -modules.
