Abstract:Solving Algebraic Equations using Coalgebra

Solving Algebraic Equations using Coalgebra

Federico deMarchi, Neil Ghani
Department of Mathematics and Computer Science, University of Leicester

Christoph Lüth
FB 3 - Mathematik und Informatik, Universität Bremen

Algebraic systems of equations define functions using recursion
where parameter passing is permitted. This generalises 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 generalises 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 generalised algebraic systems of equations have
unique solutions by replacing the traditional metric-theoretic
arguments with coalgebraic arguments.