Categories for Quantum Theory: An Introduction lays foundations for an approach to quantum theory that uses category theory, a branch of pure mathematics. Prior knowledge of quantum information theory or category theory helps, but is not assumed, and basic linear algebra and group theory suffices.

• 0: Basics


• 1: Monoidal categories


• 2: Linear structure


• 3: Dual objects


• 4: Monoids and comonoids


• 5: Frobenius structure


• 6: Complementarity


• 7: Complete positivity


• 8: Monoidal 2-categories

Chris Heunen started his undergraduate studies at the University of Nijmegen, where he received MSc degrees in both Computer Science and Mathematics, and in 2009 a PhD degree. He then did postdoctoral research at the University of Oxford and the California Institute of Technology. His work was awarded the 2012 Birkhoff-von Neumann prize for research on quantum structures. In 2015 he joined the University of Edinburgh.
Jamie Vicary did an undergraduate degree in Physics in Oxford, followed by the Part III Mathematics course in Cambridge. He did a PhD in category theory and quantum information with Christopher Isham at Imperial College London, which was awarded in 2009. Since that time he has done research into the mathematical foundations of quantum computation, with positions in Oxford, Singapore and Birmingham.