Bases for parametrized iterativity
type: Item
instance of: scholarly article
title: Bases for parametrized iterativity
zbMATH Open document ID: 1160.18003
author: Jiří Adámek
author: Stefan Milius
author: Jiří Velebil
published in: Information and Computation
publication date: 2009-03-04T00:00:00Z
review text: Parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where the recursion is allowed to use only some variables (chosen as a parameter). A generalized definition of iterative recursive system of equations for a general category of algebras is presented. An algebra is iterative if every such system has a unique solution. A functor is called finitary if it preserves all colimits of updirected diagrams. A base for a locally presentable category \(\mathcal A\) is a functor from \(\mathcal A\) into the category of all monadic algebras over finitary functors. It is proved that for every base there exists a free iterative algebra over a finitely presentable object and it can be constructed by colimit construction.
reviewed by: Václav Koubek
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 68Q70
Mathematics Subject Classification ID: 18B20
zbMATH DE Number: 5522922
zbMATH Keywords: iterative algebra
zbMATH Keywords: monad
zbMATH Keywords: iterative theory
zbMATH Keywords: parametrized signature
zbMATH Keywords: locally presentable category
MaRDI profile type: Publication
full work available at URL: j.ic.2008.05.002
OpenAlex ID: W2090818170
cites work: Q4044767
cites work: Terminal coalgebras and free iterative theories
cites work: Iterative algebras at work
cites work: Iterative algebras for a base
cites work: Algebras with parametrized iterativity
cites work: Q4293501
cites work: Coequalizers and free triples
cites work: Fundamental properties of infinite trees
cites work: A Perspective View of Discrete Automata and Their Design
cites work: Regular trees and the free iterative theory
cites work: A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on
cites work: Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads
cites work: Q4215784
cites work: Iterative algebras
cites work: Unique fixed points vs. least fixed points
cites work: Generalizing Substitution
DOI: 10.1016/J.IC.2008.05.002
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description: scientific article; zbMATH DE number 5522922