Bonn Topology Group - Abstracts

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Talk

June 24, 2025
Jaco Ruit (MPIM): Profunctor calculus for generalized ∞-categories

Abstract

In algebra, rings admit two kinds of morphisms: ring homomorphisms, and bimodules between rings. A categorical level higher, the same is true: there are functors, and profunctors between ∞-categories. More generally, analogous notions exist for different generalization of ∞-categories, such as (∞,n)-categories, enriched and internal ∞-categories, and (enriched) ∞-operads.

These generalized ∞-categories, together with their two types of arrows: functors and profunctors, assemble into an ambient 2-dimensional ∞-categorical structure. Most fundamental concepts of category theory may be developed internally to these ambient structures (such as weighted colimits, pointwise Kan extensions, and colimit completions), via their calculus of profunctors. I will illustrate this framework with several examples.

This talk is based on my Ph.D. thesis. If time permits, I will also touch on work-in-progress on colimit completions for various generalizations of ∞-categories.

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