Lawvere theories and C-systems

TL;DR

This paper establishes a categorical equivalence between l-bijective C-systems and Lawvere theories, providing a new perspective on the structure of these mathematical frameworks.

Contribution

It constructs an explicit isomorphism between the category of l-bijective C-systems and the category of Lawvere theories, linking two important categorical structures.

Findings

Proves the isomorphism between the two categories.

Provides a new categorical perspective on C-systems.

Enhances understanding of Lawvere theories in relation to C-systems.

Abstract

In this paper we consider the class of l-bijective C-systems, i.e., C-systems for which the length function is a bijection. The main result of the paper is a construction of an isomorphism between two categories - the category of l-bijective C-systems and the category of Lawvere theories.