# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 14th 2020

For completeness I have added pointer to

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.

1. Added the fact the yoneda embedding is a natural transformation.

Anonymous

• CommentRowNumber3.
• CommentAuthorHurkyl
• CommentTimeMay 24th 2021

Corrected the explanation of naturality.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeOct 9th 2021
• (edited Oct 9th 2021)

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.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeOct 9th 2021
• (edited Oct 9th 2021)

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMay 28th 2022
• (edited May 28th 2022)

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

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

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 8th 2022
• (edited Jul 8th 2022)

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.

• Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
• To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

• (Help)