  The aim of the paper is to describe autocompact objects in Ab5-categories,
i.e. objects in cocomplete abelian categories with exactness preserving
filtered colimits of exact sequences, whose covariant Hom-functor commutes with
copowers of the object itself. A characterization of non-autocompact object is
given, a general criterion of autocompactness of an object via the structure of
its endomorphism ring is presented and a criterion of autocompactness of
products is proven.
