A finite algebraic presentation of Lawvere theories in the object-classifier topos

TL;DR

This paper explores a finite algebraic presentation of Lawvere theories within the object-classifier topos, contrasting with their infinite countably-sorted algebraic nature in the sets topos, offering a new perspective on their structure.

Contribution

It introduces a finite algebraic framework for Lawvere theories in the object-classifier topos, providing a novel approach to their algebraic presentation.

Findings

Finite algebraic presentation of Lawvere theories achieved in the object-classifier topos

Contrasts with the infinite countably-sorted algebraic nature in the sets topos

Provides new insights into the structure of Lawvere theories

Abstract

Over the topos of sets, the notion of Lawvere theory is infinite countably-sorted algebraic but not one-sorted algebraic. Shifting viewpoint over the object-classifier topos, a finite algebraic presentation of Lawvere theories is considered.