Lax Colimits and Free Fibrations in \infty-Categories

  • David Gepner

  • Rune Haugseng

  • Thomas Nikolaus

    Max-Planck-Institut für Mathematik, Bonn, Germany
Lax Colimits and Free Fibrations in $\infty$-Categories cover
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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.

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David Gepner, Rune Haugseng, Thomas Nikolaus, Lax Colimits and Free Fibrations in \infty-Categories. Doc. Math. 22 (2017), pp. 1225–1266

DOI 10.4171/DM/593