# Solving algebraic equations using coalgebra

Federico De Marchi; Neil Ghani; Christoph Lüth^{[1]}

- [1] FB 3 – Mathematics and Computer Science, Universität Bremen;

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2003)

- Volume: 37, Issue: 4, page 301-314
- ISSN: 0988-3754

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topMarchi, 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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