Published: 7th August 2023
DOI: 10.4204/EPTCS.380
ISSN: 2075-2180


Proceedings Fifth International Conference on
Applied Category Theory
Glasgow, United Kingdom, 18-22 July 2022

Edited by: Jade Master and Martha Lewis

Canonical Gradings of Monads
Flavien Breuvart, Dylan McDermott and Tarmo Uustalu
Categorification of Negative Information using Enrichment
Andrea Censi, Emilio Frazzoli, Jonathan Lorand and Gioele Zardini
A Category of Surface-Embedded Graphs
Malin Altenmüller and Ross Duncan
Coend Optics for Quantum Combs
James Hefford and Cole Comfort
Compositional Modeling with Stock and Flow Diagrams
John Baez, Xiaoyan Li, Sophie Libkind, Nathaniel D. Osgood and Evan Patterson
Cornering Optics
Guillaume Boisseau, Chad Nester and Mario Román
Data Structures for Topologically Sound Higher-Dimensional Diagram Rewriting
Amar Hadzihasanovic and Diana Kessler
Dependent Optics
Pietro Vertechi
Diegetic Representation of Feedback in Open Games
Matteo Capucci
Differential 2-rigs
Fosco Loregian and Todd Trimble
Dynamic Operads, Dynamic Categories: From Deep Learning to Prediction Markets
Brandon T. Shapiro and David I. Spivak
Extending Resource Monotones using Kan Extensions
Robin Cockett, Isabelle Jianing Geng, Carlo Maria Scandolo and Priyaa Varshinee Srinivasan
Fibrational Linguistics (FibLang): Language Acquisition
Fabrizio Genovese, Fosco Loregian and Caterina Puca
Lax Liftings and Lax Distributive Laws
Ezra Schoen
Magnitude and Topological Entropy of Digraphs
Steve Huntsman
Monoidal Width: Capturing Rank Width
Elena Di Lavore and Paweł Sobociński
On the Pre- and Promonoidal Structure of Spacetime
James Hefford and Aleks Kissinger
Open Dynamical Systems as Coalgebras for Polynomial Functors, with Application to Predictive Processing
Toby St. Clere Smithe
Polynomial Functors and Shannon Entropy
David I. Spivak
Promonads and String Diagrams for Effectful Categories
Mario Román
String Diagrams for Layered Explanations
Leo Lobski and Fabio Zanasi
Unification of Modal Logic via Topological Categories
Lingyuan Ye
Universal Properties of Lens Proxy Pullbacks
Matthew Di Meglio
Value Iteration is Optic Composition
Jules Hedges and Riu Rodríguez Sakamoto


The Fifth International Conference on Applied Category Theory took place at the University of Strathclyde on 18−22 July 2022, following the previous meetings at Leiden (2018), Oxford (2019), MIT (2020, fully online), and Cambridge (2021). It was preceded by the Adjoint School 2022 (11−15 July), a collaborative research event in which junior researchers worked on cutting-edge topics under the mentorship of experts. The conference comprised 59 contributed talks, a poster session, an industry showcase session, and a session where junior researchers who had attended the Adjoint School presented the results of their research at the school. Information regarding the conference may be found at

ACT 2022 was a hybrid event, with physical attendees present in Glasgow and other participants taking part online. All talks were streamed to YouTube and with synchronous discussion on Zulip. Links to recordings of the talks as well as notes taken during the conference may be found at

Submission to ACT2022 had three tracks: extended abstracts, software demonstrations, and proceedings. The extended abstract and software demonstration submissions had a page limit of 2 pages, and the proceedings track had a page limit of 14 pages. Only papers submitted to the proceedings track were considered for publication in this volume. ACT2022 was the first year with a software demonstration track. In total, there were 97 submissions, of which 59 were accepted for presentation and 24 for publication in this volume. Publication of accepted submissions in the proceedings was determined by personal choice of the authors and not based on quality. Each submission received a review from three different members of the programming committee, and papers were selected based on discussion and consensus by these reviewers.

The contributions to ACT2022 ranged from pure to applied and included contributions in a wide range of disciplines in science and engineering. ACT2022 included talks in linguistics, functional programming, classical mechanics, quantum physics, probability theory, electrical engineering, epidemiology, thermodynamics, engineering, and logic. The quality of submissions to ACT2022 was very high, containing both cutting-edge category theory and a high degree of relevance to the chosen application. Many of the submissions had software demonstrating their work or represented work done in collaboration with industry or a scientific organization. The industry session included 10 invited talks by practitioners using category theory in private enterprise. ACT2022 was sponsored by Huawei, Protocol Labs, Cambridge Quantum, Conexus, Topos, and SICSA (Scottish Informatics and Computer Science Alliance).

ACT2022 was the first meeting since the inaugural which was not severely affected by COVID-19. The conference saw the community return in full force with more attendees, submissions, and general initiatives than previous editions of the conference. In particular, we were inspired by how many new people from a very wide range of backgrounds have joined in research with the applied category theory community. We hope that ACT, the conference and the community, continue to grow in future years. We are excited to see the new developments at ACT2023.

Jade Master and Martha Lewis
Chairs of the ACT 2022 Programme Committee