$(\infty,2)$-categories and lax colimits

Abstract: Many higher-categorical structures, most notably $(\infty,1)$-categories themselves, form $(\infty,2)$-categories. It is thus highly desirable to characterize such structures in terms of $(\infty,2)$-categorical universal properties. One recent framework allowing us to understand such $(\infty,2)$-categorical universal properties is the theory of (co)limits in $(\infty,2)$-categories. In this talk, I will explain the developing theory of (partially) lax colimits in $(\infty,2)$-categories, and discuss how it recovers a number of previous notions in the literature. I will then explain how one can generalize from the $(\infty,1)$-categorical setting to obtain a cofinality criterion for $(\infty,2)$-functors. This work was joint with Fernando Abellán.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos