Subobject classifier for algebraic structures
type: Item
instance of: scholarly article
title: Subobject classifier for algebraic structures
zbMATH Open document ID: 0636.18003
DOI: 10.1016/0021-8693(88)90092-0
author: F. Borceux
author: Barbara Veit
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Any locally presentable category \({\mathcal C}\) can be embedded (in a reasonably ``canonical'', but non-unique, way) in a topos of presheaves \({\mathcal P}\). The authors show that there exists an object \(\Omega_{{\mathcal C}}\) in \({\mathcal P}\) which plays the role of a suboject classifier for \({\mathcal C}\) (except that it does not necessarily live in \({\mathcal C}\), and they show how localizations of \({\mathcal C}\) may be classified by Lawvere- Tierney topologies on \(\Omega_{{\mathcal C}}\), extending the well-known classification when \({\mathcal C}\) itself is a (Grothendieck) topos.
Mathematics Subject Classification ID: 18C99
Mathematics Subject Classification ID: 18B25
zbMATH DE Number: 4036040
zbMATH Keywords: locally presentable category
zbMATH Keywords: topos of presheaves
zbMATH Keywords: suboject classifier
zbMATH Keywords: localizations
zbMATH Keywords: Lawvere-Tierney topologies
reviewed by: Peter Johnstone
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90092-0
OpenAlex ID: W2017349129
cites work: On locales of localizations
cites work: Sheaves, localizations, and unstable extensions: Some counterexamples
cites work: Des catégories abéliennes
cites work: Lokal präsentierbare Kategorien. (Locally presentable categories)
cites work: Adjoint Lifting Theorems for Categories of Algebras
cites work: Q4145861
cites work: FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES
cites work: Q5666704
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description: scientific article; zbMATH DE number 4036040