# Solving algebraic equations using coalgebra

• [1] FB 3 – Mathematics and Computer Science, Universität Bremen;
• Volume: 37, Issue: 4, page 301-314
• ISSN: 0988-3754

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## Abstract

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Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable categories rather than just Set; and ii) we define algebraic equations to allow right-hand sides which need not consist of finite terms. We show these generalized algebraic systems of equations have unique solutions by replacing the traditional metric-theoretic arguments with coalgebraic arguments.

## How to cite

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Marchi, Federico De, Ghani, Neil, and Lüth, Christoph. "Solving algebraic equations using coalgebra." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 37.4 (2003): 301-314. <http://eudml.org/doc/245695>.

@article{Marchi2003,
abstract = {Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable categories rather than just Set; and ii) we define algebraic equations to allow right-hand sides which need not consist of finite terms. We show these generalized algebraic systems of equations have unique solutions by replacing the traditional metric-theoretic arguments with coalgebraic arguments.},
affiliation = {FB 3 – Mathematics and Computer Science, Universität Bremen;},
author = {Marchi, Federico De, Ghani, Neil, Lüth, Christoph},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {coalgebra; recursion; category theory; algebraic system of equations; monad; locally finitely presented category; natural transformation},
language = {eng},
number = {4},
pages = {301-314},
publisher = {EDP-Sciences},
title = {Solving algebraic equations using coalgebra},
url = {http://eudml.org/doc/245695},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Marchi, Federico De
AU - Ghani, Neil
AU - Lüth, Christoph
TI - Solving algebraic equations using coalgebra
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 4
SP - 301
EP - 314
AB - Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable categories rather than just Set; and ii) we define algebraic equations to allow right-hand sides which need not consist of finite terms. We show these generalized algebraic systems of equations have unique solutions by replacing the traditional metric-theoretic arguments with coalgebraic arguments.
LA - eng
KW - coalgebra; recursion; category theory; algebraic system of equations; monad; locally finitely presented category; natural transformation
UR - http://eudml.org/doc/245695
ER -

## References

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