Discrete Lawvere theories and monads

TL;DR

This paper establishes a correspondence between strongly finitary enriched monads and discrete enriched Lawvere theories under certain conditions, and shows that such monads preserve surjections.

Contribution

It demonstrates that strongly finitary enriched monads can be characterized by discrete enriched Lawvere theories, linking algebraic structures with categorical frameworks.

Findings

Strongly finitary enriched monads correspond to discrete enriched Lawvere theories.

Monads from discrete enriched Lawvere theories preserve surjections.

The results depend on specific assumptions about enrichment and finitariness.

Abstract

We show that, under certain assumptions, strongly finitary enriched monads are given by discrete enriched Lawvere theories. On the other hand, monads given by discrete enriched Lawvere theories preserve surjections.