String diagrams for higher categories

Abstract: String diagrams are a powerful computational tool, most commonly used in the context of tensor categories and occasionally bicategories. I will talk about work in progress on extending this to higher categories. The idea is to define a semistrict n-category as something which admits composites for labeled string diagrams, much as one can define a strict n-category as something that admits composites for pasting diagrams. This notion of semistrict n-category should be more general than that of a strict n-category, but not as general as that of a weak n-category. We can show that semistrict 3-categories are the same thing as Gray categories and it is known that every weak 3-category (also called a tricategory) is equivalent to a Gray category. It is not known whether something similar holds in higher dimensions. I will also try to give an idea of the usefulness of string diagram calculus in dimensions 3 and 4, by showing how it can be used to prove coherence theorems for adjunctions.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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