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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 22nd 2010

Added Eric’s illustrations to the Idea-section at Yoneda embedding.

• CommentRowNumber2.
• CommentAuthorPeter Heinig
• CommentTimeJun 19th 2017
• (edited Jun 19th 2017)

If the Yoneda embedding of a category has a left adjoint, then that category is called a total category

in the section “Properties” which appeared wrong on two accounts:

• this is hardly a “property” of the Yoneda embedding
• the same information was (and still is) given immediately below, under “Related concepts”, which seems the right place.

Simply deleted the cited sentence.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJun 19th 2017

I’ve reverted this. I don’t know what you mean by “this is hardly a property”, and I think it makes sense to include there.

1. It’s a definition of the words “total category”, rather than a property. It does seem weird for it to appear twice in a row.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeJun 19th 2017

I view the “Related concepts” as a sort of index or summary of the other concepts that are related to this one. The fact that something is mentioned there doesn’t mean it shouldn’t appear somewhere else on the page; rather the opposite, if something is related then it should be mentioned somewhere in the main text of the page.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJun 19th 2017

Yes, the section “Related concepts” is to play the role of a link list that contains everything that a reader of that entry might also want to check out. Ideally all of these keywords would also be explained a bit in the main text.

In a case like this where the main text also does not do much more than just mention a keyword, the best solution would be to expand that line into a more comprehensive paragraph.

• CommentRowNumber7.
• CommentAuthorTodd_Trimble
• CommentTimeJun 19th 2017

When the Yoneda embedding of a category has the property of having a left adjoint, we call that category total. It’s not a property true of all Yoneda embeddings obviously, but it is a notable property. :-)

• CommentRowNumber8.
• CommentAuthorTodd_Trimble
• CommentTimeJun 19th 2017

(It may be true that many if not most “Properties” sections of nLab articles are lists of properties that are necessary consequences of the concept under discussion. If that were a universal rule, then Peter had a point. I doubt this ever came up for discussion though, and I’m not sure it’s a good idea to box ourselves in with lists of rules about formatting. One rule of thumb though has been to trust each other to write sensibly, and above all to ask first before erasing someone’s work unless it’s obviously wrong – this last I feel is very important.)

• CommentRowNumber9.
• CommentAuthorMike Shulman
• CommentTimeDec 30th 2018
• (edited Dec 30th 2018)

I edited this page (Yoneda embedding) to add a link to restricted Yoneda embedding, but the link is not showing up on the page even when I shift+reload it, although if I edit it again the link is still there in the source.

2. Thanks for letting me know. I’ll look into it later, please leave the source as it is currently (i.e. including the link that is not displaying) until then.

3. Hi Mike, I just made a trivial edit, and it went through now. I don’t know what happened there, there are no errors in the logs. Just let me know if it happens again.

• CommentRowNumber12.
• CommentAuthorMike Shulman
• CommentTimeDec 30th 2018

Ok, thanks for looking at it.