Data structures for quasistrict higher categories

TL;DR

This paper introduces efficient data structures for quasistrict higher categories, enabling practical definitions and computer-verified proofs of complex categorical properties, notably in quasistrict 4-categories.

Contribution

It provides a low-complexity, implementable framework for quasistrict higher categories and demonstrates its utility through machine-verified proofs of adjunction coherence.

Findings

Practical data structures for quasistrict 4-categories

Machine-verified proof of adjunction promotion

Low axiomatic complexity compared to traditional approaches

Abstract

We present new data structures for quasistrict higher categories, in which associativity and unit laws hold strictly. Our approach has low axiomatic complexity compared to traditional algebraic definitions of higher categories, and we use it to give a practical definition of quasistrict 4-category. It is also amenable to computer implementation, and we exploit this to give a new machine-verified algebraic proof that every adjunction of 1-cells in a quasistrict 4-category can be promoted to a coherent adjunction satisfying the butterfly equations.