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math.CT2021★ 2 cited
Autocompact objects of Ab5 categories
Josef Dvořák, Jan Žemlička
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 sequen…
math.CT2020
Connected objects in categories of -acts
Josef Dvořák, Jan Žemlička
In this paper, the categorial property of compactness of an object, i. e. commuting of the corresponding $\Hom$ functor with coproducts, is studied in categories of -acts and th…
math.CT2017
Compactness in abelian categories
Peter Kálnai, Jan Žemlička
We relativize the notion of a compact object in an abelian category with respect to a fixed subclass of objects. We show that the standard closure properties persist to hold in thi…