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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2023

    this kind of page has been missing,

    starting something with (currently just) the least general (but maybe most important) version of the definition (MacLane’s “conjugate” transformations) with a brief comment on the relation to bifibrations.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2023

    added explicit pointer (here) to where MacLane shows that conjugacy of transformations is the same as them being “mates”

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2023

    made more explicit (here) that conjugate transformations exist uniquely, and hence (here) that Cat AdjCatCat_{Adj} \to Cat is locally fully faithful.

    diff, v4, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2023

    Made more explicit (here) the statement about horizontal composition of conjugate transformations, and its page/verse number in MacLane71.

    diff, v5, current

  1. There is a typo in the (3) of defintion of conjugate natural transformations. The second vertical arrow should be in the D instead of C.

    Junhua Zheng

    diff, v8, current