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-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.
Keywords: additive category, Ab5 category, autocompact object
2020 MSC: 18E10,(18A05)
Theory and Applications of Categories, Vol. 37, 2021, No. 30, pp 979-995.