An elementary proof of the naturality of the Yoneda embedding

TL;DR

This paper provides a concise proof demonstrating the naturality of the Yoneda embedding in the context of ∞-categories and shows that the space of natural transformations identical to the Yoneda embedding is contractible.

Contribution

It offers a simplified proof of the Yoneda embedding's naturality in ∞-categories and establishes the contractibility of related natural transformation spaces.

Findings

Proof of the naturality of the Yoneda embedding for ∞-categories

The space of pointwise Yoneda natural transformations is contractible

Simplification of existing proofs in higher category theory

Abstract

We give a short proof that the Yoneda embedding is natural for $\infty$-categories, and further prove that the space of natural transformations that are, pointwise, the Yoneda embedding, is contractible.