I serve as chief executive at Topos Institute.

I am interested in the mathematics of open systems, particularly through a category theoretic lens. An introduction to my work can be found in my book An Invitation to Applied Category Theory, my DPhil thesis, or on John Baez's blog. I am also interested in the social process by which science and technology is produced, and how it impacts our lives.

I believe that mathematicians and computer scientists play a critical role in shaping today's world, and that the values our research communities uphold deserve careful attention. As part of this, I believe in actively working to improve inclusivity in category theory and mathematics at large.

I am a steering committee member of The Adjoint School, an annual research school for researchers new to the applied category theory community. I was previously an executive editor of the diamond open-access journal Compositionality from its founding in 2017 until 2023, and organised the MIT Categories Seminar from 2018 until 2020.

An Invitation to Applied Category Theory

My book (with David Spivak) is available in print or on the arXiv:

The e-book version linked above is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works. © Brendan Fong and David Spivak 2019. A print version is available here.

A course based on this book was taught at MIT in January 2019; videos are available here.

Programming with Categories

In January 2020, Bartosz Milewski, David Spivak and I taught a course at MIT on programming with categories. Videos are available here; an accompanying textbook is in draft.


Here are some papers I have written, with thanks to many wonderful collaborators:

Category theory

Logic and computation

Networks and systems

Tools for mathematics


Other writing

My articles for the Topos Institute blog can be found here.