Representations of inverse monoids by partial automorphisms
type: Item
instance of: scholarly article
title: Representations of inverse monoids by partial automorphisms
zbMATH Open document ID: 0968.20036
published in: Semigroup Forum
publication date: 2001-03-13T00:00:00Z
review text: A category \(\mathbf C\) is \((E,M)\)-structured if it has subcategories \(E\) and \(M\) such that (1) \(\text{Iso}({\mathbf C})\subseteq E\cap M\) and (2) each morphism \(f\) may be factored as \(f=em\) where \(e\in E\) and \(m\in M\) and if \(e_1m_1=f=e_2m_2\), then \(e_1=e_2u\) and \(um_1=m_2\) for a unique isomorphism \(u\). An \((E,M)\)-structured category \(\mathbf C\) is said to be properly \((E,M)\)-structured if \(E\subseteq\text{Epi}({\mathbf C})\) and \(M\subseteq\text{Mono}({\mathbf C})\). The author shows that any inverse semigroup of endomorphisms of an object in a properly \((E,M)\)-structured category may be embedded in an inverse monoid of partial automorphisms between retracts of that object.
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 20M18
zbMATH DE Number: 1545248
zbMATH Keywords: structured categories
zbMATH Keywords: inverse semigroups of endomorphisms
zbMATH Keywords: inverse monoids of partial automorphisms
author: D. G. Fitz-Gerald
reviewed by: jun. Kenneth D. Magill
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1545248