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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
added more theorems to Cartesian fibration and polished the intro slightly
a few more simple statements about behaviour under pullback at Cartesian fibration
added proposition that pullback of Cartesian fibrations is homotopy pullback to Cartesian fibration
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?
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?
Added:
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.
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