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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 24th 2010
    • (edited Mar 24th 2010)

    added more theorems to Cartesian fibration and polished the intro slightly

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 26th 2010

    a few more simple statements about behaviour under pullback at Cartesian fibration

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 2nd 2010

    added proposition that pullback of Cartesian fibrations is homotopy pullback to Cartesian fibration

    • CommentRowNumber4.
    • CommentAuthorHurkyl
    • CommentTimeDec 21st 2020
    • (edited Dec 21st 2020)

    I’ve added the evaluation map eval 0:C Δ 1Ceval_0 : C^{\Delta^1} \to C as an example of a Cartesian fibration.

    I’ve convinced myself that this is true, but surprisingly I couldn’t find any references giving it as an example. Is this a case where authors just thought it too obvious to remark upon, or have I actually overlooked something?

    diff, v36, current

    • CommentRowNumber5.
    • CommentAuthorHurkyl
    • CommentTimeDec 21st 2020

    I found a reference; I never thought to look through Lurie’s section on bifibrations for this.

    diff, v36, current

    • CommentRowNumber6.
    • CommentAuthorHurkyl
    • CommentTimeDec 21st 2020

    Improved this section to describe the comma category construction.

    diff, v36, current

    • CommentRowNumber7.
    • CommentAuthorHurkyl
    • CommentTimeMar 8th 2021

    Added a section on free fibrations.

    diff, v37, current

    • CommentRowNumber8.
    • CommentAuthorHurkyl
    • CommentTimeMar 8th 2021

    Added a definition for “cartesian functor”.

    diff, v37, current

    • CommentRowNumber9.
    • CommentAuthorHurkyl
    • CommentTimeMar 8th 2021

    Improved the statement of the free fibration to be the (infinity,2) adjunction.

    diff, v38, current

    • CommentRowNumber10.
    • CommentAuthorHurkyl
    • CommentTimeApr 2nd 2021

    Mentioned that the inclusion of cartesian fibrations in the slice category has a right adjoint.

    The proof I give takes a detour through the description of the Grothendieck construction as a tensor product… is there a more direct construction of this operation via working with the slice category?

    diff, v39, current

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeNov 3rd 2021


    Straightening and unstraightening

    There is a Quillen equivalence between the model category of cartesian fibrations and the model category of presheaves valued in quasicategories. See the article straightening functor for more information.

    diff, v40, current

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