Geodesic
Lax Colimits and Free Fibrations in $\infty$-Categories
Documenta mathematica, Tome 22 (2017), pp. 1225-1266.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We define and discuss lax and weighted colimits of diagrams in $\infty$-categories and show that the coCartesian fibration corresponding to a functor is given by its lax colimit. A key ingredient, of independent interest, is a simple characterization of the free Cartesian fibration on a functor of $\infty$-categories. As an application of these results, we prove that 2-representable functors are preserved under exponentiation, and also that the total space of a presentable Cartesian fibration between is presentable, generalizing a theorem of Makkai and Paré to the $\infty$-categories setting. Lastly, in an appendix, we observe that pseudofunctors between (2,1)-categories give rise to functors between $\infty$-categories via the Duskin nerve. setting and the Duskin nerve.
Classification : 18D30, 18A30
Keywords: fibered categories, presentable categories, lax limits and colimits 
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     title = {Lax {Colimits} and {Free} {Fibrations} in $\infty${-Categories}},
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Gepner, David; Haugseng, Rune; Nikolaus, Thomas. Lax Colimits and Free Fibrations in $\infty$-Categories. Documenta mathematica, Tome 22 (2017), pp. 1225-1266. http://geodesic.mathdoc.fr/item/DOCMA_2017__22__a16/