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nLab > Latest Changes: strict initial object

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1 to 14 of 14

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 8th 2012

    split off strict initial object from initial object (in order to be able to point to it directly from within proofs elsewhere)

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeMay 3rd 2018

    Initial objects are strict in distributive categories, not just extensive ones.

    diff, v3, current

  3. The page does not need a link to itself in the first line.

    Anonymous

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    added cross-link with “empty bundle”.

    While I was at it, I expanded out the list of examples in a more user-friendly way. And I added some basic sentences as an Idea-section.

    diff, v5, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 16th 2021

    made explicit the observation that Cartesian products with strict initial objects are again initial (here)

    diff, v8, current

  6. mentioned that this is an instance of van Kampen colimits

    Naïm Favier

    diff, v15, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2023

    This would be worth expanding on a little.

    • CommentRowNumber8.
    • CommentAuthorncfavier
    • CommentTimeFeb 2nd 2023
    I was hoping someone would! I am just learning about this myself.
    • CommentRowNumber9.
    • CommentAuthorncfavier
    • CommentTimeFeb 2nd 2023
    One subtlety is that our definition of van Kampen colimits requires pullbacks to formulate, whereas in the case of the initial object pullbacks are not needed.
    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 2nd 2023

    I am just learning about this myself.

    Then you need to state where you are learning it from.

    Maybe you are looking at Sobocinski & Heindel (2011), Exp. 4.5 (i)?

    diff, v16, current

    • CommentRowNumber11.
    • CommentAuthorncfavier
    • CommentTimeFeb 2nd 2023

    Well I was learning about van Kampen colimits, extensive categories and strict initial objects from the nLab and realised there was a connection.

    I did find a confirmation on page 35 of these slides, but the reference you found is better.

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeFeb 3rd 2023

    realised there was a connection.

    Great, so add an indication of that connection the entry. Readers will appreciate it.

    • CommentRowNumber13.
    • CommentAuthorncfavier
    • CommentTimeFeb 3rd 2023

    elaborate a bit on van Kampenness

    diff, v17, current

    • CommentRowNumber14.
    • CommentAuthorncfavier
    • CommentTimeMar 8th 2024

    Added two examples: cartesian closed categories and categories with products that distribute over the initial object.

    diff, v23, current

1 to 14 of 14

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