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Title: Automated rewriting for higher categories and applications to quantum theory
Author: Bar, Krzysztof
ISNI:       0000 0004 7229 0756
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2016
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The contribution of this thesis is a novel framework for rewriting in higher categories. Its theoretical foundation is the theory of quasistrict higher categories and the practical realisation is a proof assistant Globular. The framework introduces the notions of diagrams and signatures as new mutually-recursive structures that give the algebraic basis for the approach. These structures are related the notion of an n-polygraph, but allow reasoning about quasistrict higher categorical structures in a way amenable to computer implementation. Building on this, we propose a new definition of a quasistrict 4-category, and prove a result that in a quasistrict 4-category, an adjunction of 1-morphisms gives rise to a coherent adjunction satisfying the butterfly equations.
Supervisor: Abramsky, Samson ; Coecke, Bob Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Quantum theory ; Categories (Mathematics)