I have made more explicit in the text pointer to

for the $\infty$-Yoneda lemma over possibly large $\infty$-categories

for the $\infty$-Yoneda embedding over possibly large $\infty$-categories.

]]>added pointer to:

- Kerodon,
*The Yoneda Embedding*$[$kerodon:03JA$]$

This does seem to be formulated in the generality of large (but locally small, of course) $\infty$-categories.

]]>added pointer to:

- Emily Riehl, Dominic Verity, Def. 6.2.3 and Thm. 7.2.22 in:
*The comprehension construction*, Higher Sttructures**2**1 (2018) (arXiv:1706.10023, hs:39)

but that also speaks about Yoneda for small $\infty$-categories…

]]>This old entry needs some attention concerning how it does or does not speak regarding size issues.

Where the fully faithfulness is stated first (here) the entry does speak as if large $\infty$-categories are being considered, and I guess it should indeed hold in this generality, but the reference offered, namely HTT Prop. 5.1.3.1, speaks of small $\infty$-categories (namely simplicial sets, regarded as stand-ins for small quasi-categories).

Further down under “Naturalness” (here) large $\infty$-categories are mentioned more explicitly, and that’s now also what the reference considers (HTT, Prop. 5.3.6.10), but neither talks about fully-faithfulness at this point.

]]>Corrected the explanation of naturality.

]]>Added the fact the yoneda embedding is a natural transformation.

Anonymous

]]>For completeness I have added pointer to

- Emily Riehl, Dominic Verity, Section 6 of:
*Fibrations and Yoneda’s lemma in an $\infty$-cosmos*, Journal of Pure and Applied Algebra Volume 221, Issue 3, March 2017, Pages 499-564 (arXiv:1506.05500, doi:10.1016/j.jpaa.2016.07.003)

though there should really be some accompanying discussion of how this form of the statement is related to the usual one in terms of presheaves.

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