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We define and discuss lax and weighted colimits of diagrams in -categories and show that the coCartesian fibration associated to a functor is given by its lax colimit. A key ingredient, of independent interest, is a simple characterization of the free Cartesian fibration associated to a a functor of -categories. As an application of these results, we prove that lax representable functors are preserved under exponentiation, and also that the total space of a presentable Cartesian fibration between -categories is presentable, generalizing a theorem of Makkai and Par\'e to the -categorical setting. Lastly, in the appendix, we observe that pseudofunctors between (2,1)-categories give rise to functors between -categories via the Duskin nerve.