Syntactic characterizations of closure under pullbacks and of locally polypresentable categories
type: Item
instance of: scholarly article
title: Syntactic characterizations of closure under pullbacks and of locally polypresentable categories
zbMATH Open document ID: 0870.18002
DOI: 10.1016/S0168-0072(96)00044-9
published in: Annals of Pure and Applied Logic
publication date: 1997-09-17T00:00:00Z
review text: In the paper a characterization of a theory \(T\), which is invariant under pullbacks, is given by several equivalent conditions. One of them is that \(T\) has polypresentations. A theory \(T\) is said to be invariant under pullbacks, iff the category of models of \(T\) is closed under the construction of pullbacks. The theory of algebraically closed fields is invariant under pullbacks but not under connected limits. As a second result it is shown that any category is locally \(\omega\)-polypresentable if and only if it is equivalent to the category of models of a pullback theory. Finally it is proved that the category of models of a finitary theory which is invariant under equalizers is not in general finitely accessible.
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 03C40
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 68Q65
Mathematics Subject Classification ID: 03G30
zbMATH DE Number: 992112
zbMATH Keywords: category of structures
zbMATH Keywords: invariance under limits
zbMATH Keywords: locally presentable category
zbMATH Keywords: accessibility
zbMATH Keywords: flat functor
zbMATH Keywords: polypresentations
zbMATH Keywords: category of models
zbMATH Keywords: connected limits
zbMATH Keywords: pullback theory
author: Michel Hébert
reviewed by: Hans-Jürgen Vogel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 992112