Fraïssé limits in comma categories
type: Item
instance of: scholarly article
title: Fraïssé limits in comma categories
zbMATH Open document ID: 1426.08001
author: Christian Pech
author: Maja Pech
published in: Applied Categorical Structures
publication date: 2018-08-10T00:00:00Z
review text: This paper uses the Droste-Göbel categorical formulation of Fraïssé's theorem to produce sufficient conditions for a comma category to contain a universal homogeneous object [\textit{M. Droste} and \textit{R. Göbel}, Contemp. Math. 131, 49--74 (1992; Zbl 0759.18002)]. The main theorem is expressed in terms of 10 properties, so will not be reproduced here. Using the criterion of this theorem, the paper characterizes homogeneous structures which possess universal homogeneous endomorphisms. Finally, the paper characterizes the retracts of homogeneous structures that are induced by universal homogeneous retractions. For example, every retract of any of the following structures is induced by a universal homogeneous retraction: the countable random graph, the countable atomless Boolean algebra, the countable dense linear order, the countable generic poset, and the rational Urysohn space.
reviewed by: Keith A. Kearnes
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 18A25
Mathematics Subject Classification ID: 03C15
Mathematics Subject Classification ID: 08C05
Mathematics Subject Classification ID: 03C50
zbMATH DE Number: 6916419
zbMATH Keywords: comma category
zbMATH Keywords: homogeneous object
zbMATH Keywords: homogeneous structure
zbMATH Keywords: retract
zbMATH Keywords: endomorphism
MaRDI profile type: Publication
full work available at URL: s10485-018-9519-1
OpenAlex ID: W2793673586
cites work: Q4111746
cites work: Reconstructing the topology on monoids and polymorphism clones of the rationals
cites work: Reconstructing the topology of clones
cites work: The monoid of the random graph
cites work: Q4856547
cites work: Quasi-Banach spaces of almost universal disposition
cites work: A characterization of retracts in certain Fraïssé limits
cites work: The Bergman property for endomorphism monoids of some Fraïssé limits
cites work: The Cantor function
cites work: Q4026893
cites work: Asymmetric graphs
cites work: Q5819562
cites work: Q4336034
cites work: Fraïssé sequences: category-theoretic approach to universal homogeneous structures
cites work: Injective objects and retracts of Fraïssé limits
cites work: Q4215784
cites work: A survey of homogeneous structures
cites work: Q3118090
cites work: Intra-party decision making, party formation, and moderation in multiparty systems
cites work: On automatic homeomorphicity for transformation monoids
cites work: On polymorphism-homogeneous relational structures and their clones.
cites work: Universal graphs and universal functions
DOI: 10.1007/S10485-018-9519-1
Recommended article: Q3328710
Recommended article: Q3412765
Recommended article: Q2984109
Recommended article: Fraïssé limits of limit groups
Recommended article: Lax comma categories of ordered sets
Recommended article: Recollements, comma categories and morphic enhancements
Recommended article: Q4010778
Recommended article: Q4933938
Recommended article: Computability of Fraïssé limits
Recommended article: Q3324128
description: scientific article; zbMATH DE number 6916419