# Yoneda structures and KZ doctrines

## TL;DR

This paper explores the connection between Yoneda structures and KZ doctrines, demonstrating that for certain KZ doctrines, most Yoneda structure axioms are automatically satisfied, thus strengthening their theoretical relationship.

## Contribution

It shows that for locally fully faithful KZ doctrines with admissibility, all Yoneda structure axioms except the right ideal property are automatically fulfilled.

## Key findings

- Most Yoneda structure axioms are automatic under specified conditions
- The relationship between Yoneda structures and KZ doctrines is strengthened
- Provides conditions under which axioms are automatically satisfied

## Abstract

In this paper we strengthen the relationship between Yoneda structures and KZ doctrines by showing that for any locally fully faithful KZ doctrine, with the notion of admissibility as defined by Bunge and Funk, all of the Yoneda structure axioms apart from the right ideal property are automatic.