Autocompact objects of Ab5 categories
Category Theory
2021-02-10 v1
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 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.
Cite
@article{arxiv.2102.04818,
title = {Autocompact objects of Ab5 categories},
author = {Josef Dvořák and Jan Žemlička},
journal= {arXiv preprint arXiv:2102.04818},
year = {2021}
}