turkmath.org

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.