Sean Tull
Sean Tull
Interests
I am interested in category theory and its applications to the foundations of physics. I have developed categorical principles for reconstructing quantum theory based on a description of superpositions in categorytheoretic terms.
More broadly, my thesis explores the categorical study of operational theories of physics. This draws connections between the field of generalised probabilistic theories and categorical approaches such as categorical quantum mechanics and effectus theory. For the origin of these ideas see the preprint Operational Theories of Physics as Categories. (video, slides).
I have also explored spatial features in monoidal categories with Chris Heunen and Pau Enrique Moliner, explored in most detail in the article Tensor Topology.
Other work on categorical approaches to physics includes:
 A pictorial proof of security of quantum key distribution with Aleks Kissinger and Bas Westerbaan
 The emergence of the classical from the quantum with Bob Coecke and John Selby.
I am also intrested in pure category theory. With Chris Heunen I have studied appplications of monoidal methods from physics to general categories of relations (video, slides), and particularly those of Mal'tsev categories.
Biography
My undergraduate and masters degrees were in Mathematics at the University of Cambridge. From October 2014  June 2018 I was a DPhil student in the Department of Computer Science at the University of Oxford, supervised by Bob Coecke and Chris Heunen. From AugustOctober 2018 I was a Research Assistant in the School of Informatics at the University of Edinburgh. Since November 2018 I have returned to Oxford as a Postdoctoral researcher, as a recipient of an EPSRC Doctoral Prize.
Selected Publications

Tensor Topology (Pre−print)
Pau Enrique Moliner‚ Chris Heunen and Sean Tull
2018.
Details about Tensor Topology (Pre−print)  BibTeX data for Tensor Topology (Pre−print)  Link to Tensor Topology (Pre−print)

A Categorical Reconstruction of Quantum Theory (Pre−print)
Sean Tull
2018.
Details about A Categorical Reconstruction of Quantum Theory (Pre−print)  BibTeX data for A Categorical Reconstruction of Quantum Theory (Pre−print)  Link to A Categorical Reconstruction of Quantum Theory (Pre−print)

Quotient Categories and Phases (Pre−print)
Sean Tull
2018.
Details about Quotient Categories and Phases (Pre−print)  BibTeX data for Quotient Categories and Phases (Pre−print)  Link to Quotient Categories and Phases (Pre−print)