Abstract

Higher category theory is one of the most general approaches to compositionality, with broad and striking applications across computer science, mathematics and physics. We present a new, simple way to define higher categories, in which many important compositional properties emerge as theorems, rather than axioms. Our approach is amenable to computer implementation, and we present a new proof assistant we have developed, with a powerful graphical calculus. In particular, we will outline a substantial new proof we have developed in our setting.

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