Revisiting $(\infty,2)$-naturality of the Yoneda embedding
Category Theory
2025-12-18 v2 Algebraic Topology
Abstract
We show that the Yoneda embedding 'is' -natural with respect to the functoriality of presheaves via left Kan extension, refining the -categorical result proven independently by Haugseng-Hebestreit-Linskens-Nuiten and Ramzi, and answering a question of Ben-Moshe. As the key technical ingredient, we show that the identity functor of the -category of -categories admits only one enhancement to an -functor (namely, the identity functor).
Cite
@article{arxiv.2508.11526,
title = {Revisiting $(\infty,2)$-naturality of the Yoneda embedding},
author = {Tobias Lenz},
journal= {arXiv preprint arXiv:2508.11526},
year = {2025}
}
Comments
Final version, incorporating feedback from referee. 5 pages