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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 $eval_0 : C^{\Delta^1} \to C$ 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?

• CommentRowNumber5.
• CommentAuthorHurkyl
• CommentTimeDec 21st 2020

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

• CommentRowNumber6.
• CommentAuthorHurkyl
• CommentTimeDec 21st 2020

Improved this section to describe the comma category construction.

• CommentRowNumber7.
• CommentAuthorHurkyl
• CommentTimeMar 8th 2021

Added a section on free fibrations.

• CommentRowNumber8.
• CommentAuthorHurkyl
• CommentTimeMar 8th 2021

Added a definition for “cartesian functor”.

• CommentRowNumber9.
• CommentAuthorHurkyl
• CommentTimeMar 8th 2021

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

• 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?

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