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

Shay Ben-Moshe

doi:10.4171/dm/983

JournalsdmVol. 31, No. 2pp. 435–444

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

Shay Ben-Moshe
The Hebrew University of Jerusalem, Israel

$Uniqueness and $(\infty,2)$-naturality of Yoneda cover$

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Abstract

We show that the Yoneda embedding extends to an $(\infty, 2)$ -natural transformation. Furthermore, as such, it is uniquely determined by its value at the trivial $\infty$ -category. We also study the naturality of the Yoneda lemma in its arguments, showing that it is an isomorphism of $(\infty, 2)$ -natural transformations.

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Shay Ben-Moshe, Uniqueness and $(\infty, 2)$ -naturality of Yoneda. Doc. Math. 31 (2026), no. 2, pp. 435–444

DOI 10.4171/DM/983