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nLab > Latest Changes: natural transformation

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  1.  
    • CommentRowNumber1.
    • CommentAuthorEric
    • CommentTimeNov 5th 2009

    Asked a question at natural transformation.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2009

    I added a quick reply.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2009

    Todd has indicated the characterization of natural transformations in terms of the cartesian closed monoidal structure on Cat in the discussion section.

    I have now created a subsection in the main body of the entry on this perspective.

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeNov 5th 2009
    • CommentRowNumber5.
    • CommentAuthorEric
    • CommentTimeNov 5th 2009

    I proposed a definition for something at natural transformation. What is a good (or existing) name for it?

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2009

    replied further in the discussion there.

    I think we are talking here really about the operation that takes a 2-category to a double category. We should draw the relevant diagrams at double category, eventually.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 3rd 2019
    • (edited Apr 3rd 2019)

    Somebody alerts me that the first diagram here does not come out right. At least for me here on this phone. But we can just have a proper LaTeX implementation now anyway. Unless somebody is quicker, I’ll do it a little later.

    diff, v51, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeApr 3rd 2019

    Okay, fixed.

  9. Thanks!

  10. Add a title to the alternative definition of natural transformation and their composition in terms of arrowwise components.

    Luidnel Maignan

    diff, v54, current

    • CommentRowNumber11.
    • CommentAuthorJem Lord
    • CommentTimeNov 5th 2020

    Alternative condition for morphismwise definition and horizontal composition in terms of morphismwise definition.

    diff, v56, current

    • CommentRowNumber12.
    • CommentAuthorHurkyl
    • CommentTimeNov 7th 2020

    Typo fix. Changed “B C:=[B,C]B^C := [B,C]” to “C B:=[B,C]C^B := [B,C]”.

    diff, v57, current

  13. Replace a diagram with tikzcd

    Anonymous

    diff, v58, current

  14. added text from HoTT book

    Anonymous

    diff, v59, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2022

    Please, what you just added is the standard classical definition. This has nothing to do with HoTT. The edit should be reverted.

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2022

    have reverted the edit from #14 (see also the discussion here)

    diff, v60, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeMar 31st 2023

    added pointer to Borceux, here and in related entries

    diff, v61, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeMay 20th 2023

    added pointer to:

    diff, v64, current

1 to 18 of 18

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