We define and discuss lax and weighted colimits of diagrams in ∞-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 ∞-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

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... entable, generalizing a theorem of Makkai and Paré to the ∞-categories setting. Lastly, in an appendix, we observe that pseudofunctors between (2,1)-categories give rise to functors between ∞-categories via the Duskin nerve. setting and the Duskin nerve.