Projective and injective objects of the categories dual to \mathfrak{A}\mathfrak{B}

The categories dual to the category of Abelian groups (including the category of compact Abelian groups) are considered. In these categories, structure theorems on injective and projective objects are proved, and some projective coverings are calculated. In the category of compact Abelian groups, the notion of connected hull is introduced; some results on connected hulls are obtained and examples are given. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 168–182.