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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 30th 2019

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

    diff, v16, current

    • CommentRowNumber2.
    • CommentAuthorMarc
    • CommentTimeOct 2nd 2019

    added link to pdf of isbells’s 1964 article

    diff, v17, current

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

    Jonas Frey

    diff, v20, current

    • 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

      Related concepts
    • 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.

    diff, v21, current

    • 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.

    diff, v22, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 4th 2021


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

    diff, v23, current

    • CommentRowNumber11.
    • CommentAuthorvarkor
    • CommentTimeJul 20th 2021

    Mention equivalent characterisation of density in terms of lan iilan_i i being the identity.

    diff, v24, current

    • CommentRowNumber12.
    • CommentAuthorvarkor
    • CommentTimeJul 21st 2021

    Added a characterisation of density in terms of cocompletions.

    diff, v26, current

    • CommentRowNumber13.
    • CommentAuthorGuest
    • CommentTimeJul 23rd 2021

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

    • CommentRowNumber14.
    • CommentAuthorvarkor
    • CommentTimeMay 3rd 2023
    • CommentRowNumber15.
    • CommentAuthorvarkor
    • CommentTimeJun 25th 2023

    Added another characterisation of density.

    diff, v32, current

    • CommentRowNumber16.
    • CommentAuthorvarkor
    • CommentTimeDec 21st 2023

    Added the example of small VV-categories in large VV-categories.

    diff, v33, current