An elementary proof of the naturality of the Yoneda embedding

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.

arXiv comment7 pages, comments welcome ! v3: changed the title following a suggestion from the referee; added a paragraph about uniqueness; rewrote the introduction to require less background; and finally made some minor modifications. This is the accepted version. Now 10 pages