Title of article
Flatness properties of acts over semigroups
Author/Authors
Laan, Valdis University of Tartu - Narva mnt 18 - Tartu, Estonia , Reimaa, Ülo University of Tartu - Narva mnt 18 - Tartu, Estonia , Tart, Lauri University of Tartu - Narva mnt 18 - Tartu, Estonia , Teor, Elery Hotel Tartu - Soola 3 - Tartu, Estonia
Pages
34
From page
59
To page
92
Abstract
In this paper we study flatness properties (pullback flatness,
limit flatness, finite limit flatness) of acts over semigroups. These are defined
by requiring preservation of certain limits from the functor of tensor multiplication
by a given act. We give a description of firm pullback flat acts
using Conditions (P) and (E). We also study pure epimorphisms and their
connections to finitely presented acts and pullback flat acts. We study these
flatness properties in the category of all acts, as well as in the category of
unitary acts and in the category of firm acts, which arise naturally in the
Morita theory of semigroups.
Keywords
Act over semigroup , pullback flatness , finite limit flatness , pure epimorphism , finitely presentable act , firm act , sequence act
Journal title
Categories and General Algebraic Structures with Applications
Serial Year
2021
Record number
2667977
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