Completeness of cocompletions
type: Item
instance of: scholarly article
title: Completeness of cocompletions
zbMATH Open document ID: 1068.18002
author: Panagis Karazeris
author: Jiří Rosický
author: Jiří Velebil
published in: Journal of Pure and Applied Algebra
publication date: 2005-04-07T00:00:00Z
review text: We know well that the existence of (finite) limits in a free cocompletion of a category \(\mathcal C\) under (finite) colimits is not automatically guaranteed. The existence of such limits is a kind of a weak completeness condition on the category \(\mathcal C\). The authors propose several weak completeness concepts. Then they show that all these concepts are equivalent in the sense that if the cone functors of all finite diagrams in a category satisfy simultaneously one of the proposed finiteness conditions, then they simultaneously satisfy any of them. The established equivalence of limit concepts is used so as to derive results on the existence of limits in colimit cocompletions. It turns out that there is a crucial difference according as we consider finite diagrams or \(\alpha\)-small ones for uncountable \(\alpha\).
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 18A35
Mathematics Subject Classification ID: 18C35
zbMATH DE Number: 2153394
zbMATH Keywords: cocompletion
zbMATH Keywords: limit
zbMATH Keywords: weak completeness condition
zbMATH Keywords: category
MaRDI profile type: Publication
full work available at URL: j.jpaa.2004.08.019
OpenAlex ID: W1998115557
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DOI: 10.1016/J.JPAA.2004.08.019
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description: scientific article; zbMATH DE number 2153394