Axioms for the category of sets and relations

TL;DR

This paper introduces axioms for the dagger category of sets and relations, drawing parallels with axioms used for the dagger category of Hilbert spaces and bounded operators, to formalize their structure.

Contribution

It presents a new set of axioms for the category of sets and relations that align with those used for Hilbert spaces, bridging categorical structures.

Findings

Axioms formalize the dagger category of sets and relations.

Connections established between set-relations and Hilbert space axioms.

Provides a foundation for further categorical analysis of relations.

Abstract

We provide axioms for the dagger category of sets and relations that recall recent axioms for the dagger category of Hilbert spaces and bounded operators.