Objects with closed diagonals
type: Item
instance of: scholarly article
title: Objects with closed diagonals
zbMATH Open document ID: 0651.18002
DOI: 10.1016/0022-4049(88)90083-7
author: Sandra Mantovani
author: Walter Tholen
author: Eraldo Giuli
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathfrak C}\) be a category with finite products, \({\mathfrak B}^ a \)subcategory, M a class of monomorphisms and \(\Delta\) (X): \(X\to X\times X\). The authors study conditions such that a diagonal property of the type \(X\in {\mathfrak B}\Leftrightarrow \Delta (X)\in M\) holds. For example: Let \({\mathfrak A}\) be a reflective subcategory, r its reflector, k(T,X) the canonical morphism r(T\(\times X)\to r(T)\times r(X)\), M the class of equalizers of any two morphisms into an object of \({\mathfrak A}\) and \({\mathfrak B}\) the category of all subobjects of objects of \({\mathfrak A}\). Then, if k(T,X) is mono for all \(t\in {\mathfrak C}\), X belongs to \({\mathfrak B}\) if and only if \(\Delta\) (X)\(\in M\).
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18A32
zbMATH DE Number: 4061466
zbMATH Keywords: monomorphisms
zbMATH Keywords: diagonal property
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90083-7
OpenAlex ID: W1978476133
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description: scientific article; zbMATH DE number 4061466