Abstract
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, whose covariant Hom-functor commutes with copowers of the object itself. A characterization of non-auto compact 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.