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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2023
    • (edited May 5th 2023)

    this kind of entry has been missing: On (versions of) the 2-category of categories with adjoint functors between them.

    Starting here some minimum, for the moment just copying the paragraphs that I just added at transformation of adjoints

    v1, current

    • CommentRowNumber2.
    • CommentAuthorHurkyl
    • CommentTimeMay 5th 2023
    • (edited May 5th 2023)

    In the infinity category case, Higher Topos Theory has the basic elements, although it only spells things out in the case of presentable fibrations. I packaged them together at https://ncatlab.org/nlab/show/adjoint+(infinity%2C1)-functor#category_of_adjunctions . (the term “adjunct fibration” is my own)

    I added a link to the related concepts.

    Incidentally, in HTT, Lurie uses “bifibration” to refer to fibrations over C×DC \times D corresponding, under a two-variable version of the Grothendieck construction, to bifunctors C op×DGpdC^{op} \times D \to \infty Gpd, if I’ve worked through everything correctly. So it may be confusing to import similar language over to that article.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 5th 2023

    Lurie uses “bifibration” to refer to fibrations over C×DC \times D

    This is related to the point that BryceClark just made in another thread: here. For these structures we should probably point to two-sided fibration,

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2023

    added pointer to p. 102 in MacLane71

    diff, v6, current