A criterion for the existence of subobject classifiers
type: Item
instance of: scholarly article
title: A criterion for the existence of subobject classifiers
zbMATH Open document ID: 0921.18002
author: Hiroshi Watanabe
published in: Hokkaido Mathematical Journal
publication date: 1999-09-26T00:00:00Z
review text: The author observes that if \(\mathcal E\) is a cocomplete category having a small dense subcategory \(\mathcal C\), `the subobject classifier of \(\mathcal E\)' may always be considered to exist as a presheaf on \(\mathcal C\). He shows that \(\mathcal E\) has a subobject classifier if and only if this presheaf lies in \(\mathcal E\) considered as a reflective subcategory of the presheaf category. A couple of variants of this condition are given. These results are closely related to those of \textit{F. Borceux} and \textit{B. Veit} [``Subobject classifier for algebraic structures'', J. Algebra 112, No. 2, 306-314 (1988; Zbl 0636.18003)].
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 68Q55
zbMATH DE Number: 1292207
zbMATH Keywords: cocomplete category
zbMATH Keywords: subobject classifier
zbMATH Keywords: reflective subcategory
zbMATH Keywords: presheaf category
reviewed by: Peter Johnstone
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001081
OpenAlex ID: W2096282096
DOI: 10.14492/HOKMJ/1351001081
description: scientific article; zbMATH DE number 1292207