Vicary abstract and references

We propose a new definition of quasistrict 4-category, and use it to prove that every weak adjunction of 1-morphisms in a semistrict 4-category can be promoted to a strong adjunction satisfying the butterfly equations (formalized proof available at http://globular.science/1605.002). We believe this to be the first nontrivial proof to be formulated in an algebraic 4-category. Our definition is simpler than some previous definitions, with many standard axioms of higher categories emerging instead as properties. Our definition is also amenable to computer formalization, and we introduce our new web-based proof assistant, GLOBULAR, which aims to make compositional proofs in higher category theory easy to construct and visualize.

 

Krzysztof Bar and Jamie Vicary (2016), "Data structures for quasistrict higher categories", https://arxiv.org/abs/1610.06908

 

Krzysztof Bar, Aleks Kissinger and Jamie Vicary (2016), "Globular: an online proof assistant for higher-dimensional rewriting", https://arxiv.org/abs/1612.01093

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