Published: 8th February 2021
DOI: 10.4204/EPTCS.333
ISSN: 2075-2180


Proceedings of the 3rd Annual International
Applied Category Theory Conference 2020
Cambridge, USA, 6-10th July 2020

Edited by: David I. Spivak and Jamie Vicary

David I. Spivak and Jamie Vicary
The Safari of Update Structures: Visiting the Lens and Quantum Enclosures
Matthew Wilson, James Hefford, Guillaume Boisseau and Vincent Wang
A Monad for Probabilistic Point Processes
Swaraj Dash and Sam Staton
Symmetric Monoidal Categories with Attributes
Spencer Breiner and John S. Nolan
Wiring diagrams as normal forms for computing in symmetric monoidal categories
Evan Patterson, David I. Spivak and Dmitry Vagner
Open Diagrams via Coend Calculus
Mario Román
A diagrammatic approach to symmetric lenses
Bryce Clarke
The more legs the merrier: A new composition for symmetric (multi-)lenses
Michael Johnson and Robert Rosebrugh
Cyber Kittens, or Some First Steps Towards Categorical Cybernetics
Toby St Clere Smithe
Compositional Cyber-Physical Systems Modeling
Georgios Bakirtzis, Christina Vasilakopoulou and Cody H. Fleming
A Compositional Sheaf-Theoretic Framework for Event-Based Systems
Gioele Zardini, David I. Spivak, Andrea Censi and Emilio Frazzoli
Double Categories of Open Dynamical Systems (Extended Abstract)
David Jaz Myers
Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality (Extended Abstract)
Lachlan McPheat, Mehrnoosh Sadrzadeh, Hadi Wazni and Gijs Wijnholds
DisCoPy: Monoidal Categories in Python
Giovanni de Felice, Alexis Toumi and Bob Coecke
Compositional Game Theory, Compositionally
Robert Atkey, Bruno Gavranović, Neil Ghani, Clemens Kupke, Jérémy Ledent and Fredrik Nordvall Forsberg
The linear-non-linear substitution 2-monad
Martin Hyland and Christine Tasson
Proof Theory of Partially Normal Skew Monoidal Categories
Tarmo Uustalu, Niccolò Veltri and Noam Zeilberger
Reverse Derivative Ascent: A Categorical Approach to Learning Boolean Circuits
Paul Wilson and Fabio Zanasi
Operations on Metric Thickenings
Henry Adams, Johnathan Bush and Joshua Mirth
Behavioral Mereology: A Modal Logic for Passing Constraints
Brendan Fong, David Jaz Myers and David I. Spivak
Categorical semantics of a simple differential programming language
Geoffrey Cruttwell, Jonathan Gallagher and Dorette Pronk
Functorial Language Games for Question Answering
Giovanni de Felice, Elena Di Lavore, Mario Román and Alexis Toumi
Computational Adequacy for Substructural Lambda Calculi
Vladimir Zamdzhiev
Dualizing sup-preserving endomaps of a complete lattice
Luigi Santocanale
Products in a Category with Only One Object
Richard Statman


Following the inaugural meeting in Leiden, Holland and a successful event in Oxford, UK, the third annual International Applied Category Theory Conference (ACT2020) was planned to take place at MIT in Cambridge, Massachusetts USA. However, the global COVID-19 pandemic made the prospect of holding a large in-person meeting impossible. While many 2020 conferences were being canceled, the local organizing committee—and in particular the technical lead Paolo Perrone—both foresaw the seriousness of the pandemic and the possibility of pivoting to a completely online conference, and was able to reverse course quite seamlessly.

The event was thus held completely online. While this had a rather large effect on our ability to interact and collaborate with one another, the number and quality of contributions was almost identical to previous years. Moreover, holding the talks online had the new benefits of reducing carbon footprint, being inclusive of people from more parts of the world, and producing higher-quality video talks, which have been posted online for posterity.

The ACT2020 contributions spanned a broad spectrum of subjects and application areas, and they ranged from quite pure to quite applied. Probably the most popular mathematical subject this year was that of lenses and their generalizations, which were discussed both on a formal level and in applications to databases, dynamical systems, functional programming, game theory, and neuroscience. Also popular were sheaf- and topos-theoretic techniques, used to model compositionality of behavior in cyberphysical, event-based systems, and even more general systems. Categorical probability and statistics was a major theme, with some new advances in stochastic processes, probabilistic programming, and general theory. There was also new work on natural language processing, categorical quantum mechanics, and the interactions between the two subjects.

Many other topics were represented at the conference, including a categorical interpretation of the work of C.S. Pierce, a new algorithm for learning Boolean circuits, and advances in topological data analysis. Of special interest was work on producing software tools for applied category theory, including both a Python library for modeling monoidal categories and a Julia library for compositional scientific computing.

Papers in this Proceedings volume represents about half of the talks presented at ACT2020. Being included in the proceedings vs. not is not an indication of talk quality, but instead almost exclusively the choice of the authors, e.g. to present work already published elsewhere. We hope that readers of this volume enjoy this representative selection and check out the other talks recorded online (a link can be found at, and we look forward to seeing you at the next event!

David Spivak and Jamie Vicary
Co-chairs of the ACT2020 Scientific Committee