I am interested in category theoretic modelling of open systems. An introduction to my work can be found on John Baez's blog, my DPhil thesis, or my book An Invitation to Applied Category Theory.
I am an executive editor of Compositionality, and organise the MIT Categories Seminar.
An Invitation to Applied Category Theory
My book (with David Spivak) will be available in Summer 2019.- B. Fong, D. Spivak, 'An Invitation to Applied Category Theory: Seven sketches in compositionality', Cambridge University Press 2019, arXiv:1803.05316.
A course based on this book was taught at MIT in January 2019; videos are available here.
Papers
Here are some papers I have written:
- B. Fong, D. Spivak, 'Graphical regular logic', arXiv:1812.05765.
- B. Fong, M. Sarazola, 'A recipe for black box functors', arXiv:1812.03601.
- B. Fong, D. Spivak, 'Hypergraph categories', arXiv:1806.08304.
- B. Fong, D. Myers, D. Spivak, 'Behavioral mereology', arXiv:1811.00420.
- B. Fong, D. Spivak, R. Tuyeras, 'Backprop as functor: a compositional perspective on supervised learning', arXiv:1711.10455.
- B. Fong, F. Zanasi, 'Universal constructions for (co)relations: categories, monoidal categories, props', arXiv:1710.03894.
- B. Fong, 'Decorated corelations', Theory and Applications of Categories, Vol. 33, 2018, No. 22, pp. 608--643, arXiv:1703.09888.
- B. Fong, F. Zanasi, 'A universal construction for (co)relations', CALCO 2017, arXiv:1703.08247.
- B. Fong: 'The algebra of open and interconnected systems', DPhil thesis, University of Oxford (2016), arXiv:1609.05382.
- B. Coya, B. Fong: 'Corelations are the prop for extraspecial commutative Frobenius monoids', Theory and Applications of Categories, Vol. 32, 2017, No. 11, pp. 380-395, arXiv:1601.02307.
- B. Fong, P. Sobocinski, P. Rapisarda: 'A categorical approach to open and interconnected systems', Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), (2016), arXiv:1510.05076.
- J. C. Baez, B. Fong, B. Pollard: 'A compositional framework for Markov processes', Journal of Mathematical Physics, 57 (2016), 033301, arXiv:1508.06448.
- J. C. Baez, B. Fong: 'A compositional framework for passive linear networks', arXiv:1504.05625.
- B. Fong: 'Decorated cospans', Theory and Applications of Categories, Vol. 30, 2015, No. 33, pp. 1096--1120, arXiv:1502.00872.
- B. Fong, H. Nava Kopp: 'Additive monotones for resource theories of parallel combinable processes', Electronic Proceedings in Theoretical Computer Science (QPL 2015), 195 (2015), pp. 170--178, arXiv:1505.02651.
- B. Fong: 'A note on interleaved quantum teleportation', Technical Report CS-RR-14-09, University of Oxford (2014), available here.
- J. C. Baez, B. Fong: 'Quantum techniques for studying equilibrium in chemical reaction networks', Journal of Complex Networks (2014), doi: 10.1093/comnet/cnu013, arXiv:1305.4988.
- J. C. Baez, B. Fong: 'A Noether theorem for Markov processes', Journal of Mathematical Physics 54 (2013), 013301, arXiv:1203.2035.
- B. Fong: 'Causal theories: a categorical perspective on Bayesian networks', Master's thesis, University of Oxford (2012), arXiv:1301.6201.
- B. Fong: 'On families of elliptic curves', Honours thesis, Australian National University and National University of Singapore (2010), available here.
Selected Talks
- 'Hypergraph categories as cospan algebras', Category Theory 2018, 8-14 July 2018. slides
- 'Backprop as functor', 2nd Workshop on Open Games, 4-6 July 2018. slides
- 'Decorated cospans', Special Session on Applied Category Theory, AMS Fall Western Sectional, University of California Riverside, 4-5 November 2017. slides
- 'Constructing categories of corelations', Category Theory Octoberfest, Carnegie Mellon University, 28-29 October 2017. slides