Revisiting $(\infty ,2)$-naturality of the Yoneda embedding

Abstract

We show that the Yoneda embedding 'is' $(\infty ,2)$-natural with respect to the functoriality of presheaves via left Kan extension, refining the $(\infty ,1)$-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 $(\infty ,1)$-category of $(\infty ,1)$-categories admits only one enhancement to an $(\infty ,2)$-functor (namely, the identity functor).

Final version, incorporating feedback from referee. 5 pages

References in corpus (1)

• Uniqueness and $(\infty ,2)$-Naturality of Yoneda