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

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 $(\infty,2)$-nat...

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Bibliographic Details
Main Author Ben-Moshe, Shay
Format Journal Article
LanguageEnglish
Published 14.05.2024
Subjects
Mathematics - Algebraic Topology
Mathematics - Category Theory
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Summary: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.
DOI:10.48550/arxiv.2405.08799