2025/08/15 by Lenz, Tobias
Mathematics · #18N65 (Primary) #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2508.11526
openalex publication_date 2025/08/15 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28
We show that the Yoneda embedding 'is' (∞,2)-natural with respect to the functoriality of presheaves via left Kan extension, refining the (∞,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 (∞,1)-category of (∞,1)-categories admits only one enhancement to an (∞,2)-functor (namely, the identity functor).