I am interested in category theoretic modelling of open systems.
Here are some papers I have written:
- B. Fong, D. Spivak, 'Hypergraph categories', arXiv:1806.08304.
- B. Fong, D. Spivak, 'Seven sketches in compositionality: An invitation to applied category theory', arXiv:1803.05316.
- 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.
Here are some talks I have given:
- '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