Finitely Presentable Algebras For Finitary Monads

TL;DR

This paper characterizes finitely presentable objects in the category of algebras for finitary regular monads on locally finitely presentable categories, extending classical algebraic notions to a categorical setting.

Contribution

It provides a categorical characterization of finitely presentable algebras for finitary regular monads, linking algebraic presentation with categorical properties.

Findings

Finitely presentable T-algebras are those with finitely many generators and relations.

The characterization extends classical algebraic notions to a categorical framework.

Provides a basis for understanding algebraic structures in enriched categorical contexts.

Abstract

For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by finitely many generators and finitely many relations.