Essential pure monomorphisms of sheaves of group actions.
type: Item
instance of: scholarly article
title: Essential pure monomorphisms of sheaves of group actions.
zbMATH Open document ID: 1205.20065
author: Mahdie Haddadi
author: M. Mehdi Ebrahimi
published in: Semigroup Forum
publication date: 2010-07-06T00:00:00Z
review text: Here are studied various notions of essentiality in the category \(\mathbf G\text{-}\mathbf{ShX}\) of sheaves -- multigroup \(G\) acts on multisets on a topological space \(X\). Let \(\mathcal M\) be the class of affine, stalk or quasi-pure \(G\)-monomorphisms in \(\mathbf G\text{-}\mathbf{ShX}\); \(f\in\mathcal M\) is called \(\mathcal M\)-essential if \(gf\in\mathcal M\) implies \(g\in\mathcal M\); weak \(\mathcal M\)-essential if \(gf\in\mathcal M\) implies that \(g\) is monic; essential \(\mathcal M\)-monomorphism if \(g\) is a monomorphism whenever \(gf\) is a monomorphism. Properties of these types of essentiality are investigated; it is shown that an \(\mathcal M\)-monomorphism \(f\) is \(\mathcal M\)-essential iff there exists a cover of disjoint open sets of \(X\) such that the restriction of \(f\) to components is \(\mathcal M\)-essential.
reviewed by: Jaak Henno
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 18A30
zbMATH DE Number: 5730954
zbMATH Keywords: purity
zbMATH Keywords: essential extensions
zbMATH Keywords: sheaves
zbMATH Keywords: acts
MaRDI profile type: Publication
full work available at URL: s00233-010-9212-7
OpenAlex ID: W2137977482
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DOI: 10.1007/S00233-010-9212-7
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description: scientific article; zbMATH DE number 5730954