Flatness properties of acts over semigroups

Autor:	Valdis Laan, Ülo Reimaa, Lauri Tart, Elery Teor
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	act over semigroup pullback flatness finite limit flatness pure epimorphism finitely presentable act firm act sequence act Mathematics QA1-939
Zdroj:	Categories and General Algebraic Structures with Applications, Vol 15, Iss 1, Pp 59-92 (2021)
Druh dokumentu:	article
ISSN:	2345-5853 2345-5861
DOI:	10.52547/cgasa.15.1.59
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/5f8a87da71334e2a867fd582f89c7136 Zobrazit plný text záznamu View record in DOAJ