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    • CommentRowNumber1.
    • CommentAuthorspitters
    • CommentTimeFeb 4th 2017

    equifibered natural transformation misses references. I’ve traced cartesian natural transformation back to: Street - the petit topos of globular sets which refers to: Carboni, Johnstone - Connected limits, familial representability and Artin glueing unfortunately, I do not have access to the latter.

    Is this the best source?

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 4th 2017

    It’s a good source, yes. My memory is that Tom Leinster’s book on higher categories also treats cartesian transformations, and it’s easily available.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 4th 2017

    Hopefully one of you finds a minute to add the reference to the entry!

    • CommentRowNumber4.
    • CommentAuthorCharles Rezk
    • CommentTimeFeb 4th 2017
    • (edited Feb 4th 2017)

    I’ve used the phrase “equifibered map” (where the map is itself a natural transformation) in various places, with this meaning (but in an \infty-context). For instance, in my old model topos notes, or here:

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 5th 2017

    References now added.

    • CommentRowNumber6.
    • CommentAuthorspitters
    • CommentTimeFeb 5th 2017

    Thanks! To be sure, is this notion indeed different from the notion of cartesian natural transformation in the theory of fibred categories. E.g. Streicher.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2017

    Thanks, Todd!

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeFeb 5th 2017
    • (edited Feb 5th 2017)

    I have also added pointer to Rezk 10 and Rezk 14.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTime4 days ago
    • (edited 4 days ago)

    I have added the statement (here) of descent in \infty-toposes characterized via equifibered transformations of colimiting diagrams

    But I am going to give this sub-section its stand-alone entry now, and then re-!include it, because the same discussion ought to be included in various other relevant entries

    diff, v5, current

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