On projective and injective objects of the categories dual to $\mathfrak{AB}$

The categories are considered dual to the category of abelian groups (including the category of compact abelian groups). In those categories the structure theorems on injective and projective objects are proved; some projective covers are calculated. In the category of compact abelian groups the notion of connective hull is introduced; some results on connective hulls are received; the examples are given.