Subpullback flat \(S\)-posets need not be subequalizer flat.
type: Item
instance of: scholarly article
title: Subpullback flat \(S\)-posets need not be subequalizer flat.
zbMATH Open document ID: 1171.20039
author: Sydney Bulman-Fleming
published in: Semigroup Forum
publication date: 2009-04-29T00:00:00Z
review text: A right \(S\)-poset \(A_S\) is called `subpullback flat' (resp. `subequalizer flat') if the functor \(A_S\otimes-\) preserves subpullbacks (resp. subequalizers). It is proved that if \(S\) is a non-trivial, commutative, cancellative pomonoid in which 1 is the greatest element, then the one-element \(S\)-poset \(\Theta_S\) is subpullback flat but is not subequalizer flat. A new proof of the fact that a pullback flat \(S\)-act is equalizer flat is presented as well.
reviewed by: Peeter Normak
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 5549500
zbMATH Keywords: ordered monoids
zbMATH Keywords: \(S\)-posets
zbMATH Keywords: flatness
zbMATH Keywords: po-acts
zbMATH Keywords: categories of acts
zbMATH Keywords: pullbacks
zbMATH Keywords: equalizers
zbMATH Keywords: partially ordered acts
MaRDI profile type: Publication
full work available at URL: s00233-008-9051-y
OpenAlex ID: W2101129429
cites work: On equalizer-flat and pullback-flat acts
cites work: Monoids, acts and categories. With applications to wreath products and graphs. A handbook for students and researchers
cites work: Pullback-Flat Acts are Strongly Flat
cites work: Absolute flatness and amalgams in pomonoids
cites work: Lazard's Theorem for S ‐posets
cites work: Flatness Properties of S-Posets
DOI: 10.1007/S00233-008-9051-Y
description: scientific article; zbMATH DE number 5549500