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

• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeSep 30th 2019

Moved the reference to the Lawvere commentary on Isbell to ’References’.

• CommentRowNumber2.
• CommentAuthorMarc
• CommentTimeOct 2nd 2019

added link to pdf of isbells’s 1964 article

1. Added warning that dense functors are not closed under composition.

Jonas Frey

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 17th 2021

Thanks. But allow me to suggest that a 2-line comment should be a Remark (\begin{remark} comment \end{remark}) and not a section all by itself.

I was going to fix it, merging it with the other “warning” to a list of remarks. But I am unsure where that other warning ends and where maybe some new definitions begins and what it really means.

If you know, please have a look, maybe you can clean this up.

We have available a beautiful list of numbered environments to help with organizing material in a transparent way:

  \begin{definition} ... \end{definition}

\begin{remark} ... \end{remark}

\begin{proposition} ... \end{proposition}

\begin{proof} ... \end{proof}


Let’s make ample use of this. It helps not only the reader to read, but also the author to organize their thoughts.

In contrast, sections should by-and-large stick to the pattern

  Idea

Definition

Properties

Examples

Related concepts

References

• CommentRowNumber5.
• CommentAuthorDmitri Pavlov
• CommentTimeMar 17th 2021
• (edited Mar 17th 2021)
Re #4: Urs, could you your list of sections to the editing sidebar? This way it would be easy to pull out when creating a new article. Otherwise, having to look up these instructions, which are buried in an obscure thread on the nForum, is quite difficult.
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMar 18th 2021

So that’s what the Template page is meant to be for, that is linked to from How to organize and write content.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeMar 18th 2021

I have tried to brush up the entry:

1. Gave the definition a numbered environment and a label, so that it can be pointed to;

2. removed the section “Warning”, moving its content to dense subcategory

(the section contained an alternative definition of “dense subcategory” – maybe the two entries want to be merged, but I won’t look into that now)

3. made the “other warning”, on the class of dense functors not being closed under composition a numbered remark,

4. made the counter-example that proved this claim a numbered example.

• CommentRowNumber8.
• CommentAuthorJonasFrey
• CommentTimeMar 18th 2021

Re #4: Thanks for the suggestions, Urs, sorry I saw them only now. I’ll try to follow your stylistic guidelines in the future.

• CommentRowNumber9.
• CommentAuthorTim Campion
• CommentTimeMay 4th 2021

Added a few examples.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeMay 4th 2021

Thanks!

I have made your Ind category a redirect, so that it points as expected; and I have hyperlinked categories of sheaves.

• CommentRowNumber11.
• CommentAuthorvarkor
• CommentTimeJul 20th 2021

Mention equivalent characterisation of density in terms of $lan_i i$ being the identity.

• CommentRowNumber12.
• CommentAuthorvarkor
• CommentTimeJul 21st 2021

Added a characterisation of density in terms of cocompletions.

• CommentRowNumber13.
• CommentAuthorGuest
• CommentTime7 days ago

Newbie question related to the last edit: is there an example of a non-pointwise density comonad isomorphic to the identity?

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