Algebraic Language Theory for Eilenberg--Moore Algebras

TL;DR

This paper introduces an algebraic language theory based on Eilenberg--Moore algebras, extending previous frameworks to include infinitely many sorts and linking to logic through definable algebras.

Contribution

It develops a new algebraic language theory supporting infinitely many sorts and establishes a connection to logic via definable algebras.

Findings

Supports algebras with infinitely many sorts

Connects algebraic structures to logical definability

Extends previous algebraic language frameworks

Abstract

We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic in form of so-called `definable algebras'.