Accessibility and the solution set condition
type: Item
instance of: scholarly article
title: Accessibility and the solution set condition
zbMATH Open document ID: 0817.18004
DOI: 10.1016/0022-4049(94)00035-H
published in: Journal of Pure and Applied Algebra
publication date: 1995-04-10T00:00:00Z
review text: It was observed by \textit{M. Makkai} and \textit{R. Paré} [``Accessible categories'', Contemp. Math. 104 (1989; Zbl 0703.03042)] that given accessible categories \({\mathcal K}\) and \({\mathcal L}\), every accessible functor \(F : {\mathcal K} \to {\mathcal L}\) satisfies the solution-set condition. In the present paper the authors prove that, conversely, the solution-set condition guarantees that \(F\) is accessible. This result requires, in fact is equivalent to, the large cardinal Vopenka's principle.
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18B15
zbMATH DE Number: 741485
zbMATH Keywords: accessible categories
zbMATH Keywords: solution-set condition
zbMATH Keywords: Vopenka's principle
author: Jiří Rosický
author: Walter Tholen
reviewed by: Jiří Adámek
MaRDI profile type: Publication
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full work available at URL: 0022-4049(94)00035-h
OpenAlex ID: W2072741434
description: scientific article; zbMATH DE number 741485