Computer Laboratory, University of Cambridge • 12-16 July 2021

Latest Updates

The 4th International Conference on Applied Category Theory will take place at the Computer Laboratory of the University of Cambridge on 12-16 July 2021, preceded by the Adjoint School 2021 on 5-9 July. This conference follows previous events at MIT, Oxford and Leiden.

The conference will be a hybrid event, with physical attendees present in Cambridge, and other participants taking part online. Due to the need for physical distancing, the number of in-person registrations will be limited, so please don't book your travel or accommodation until your registration is confirmed.

Applied category theory is a topic of interest for a growing community of researchers, interested in studying many different kinds of systems using category-theoretic tools. These systems are found across computer science, mathematics, and physics, as well as in social science, linguistics, cognition, and neuroscience. The background and experience of our members is as varied as the systems being studied. The goal of Applied Category Theory is to bring researchers in the field together, disseminate the latest results, and facilitate further development of the field.

We accept contributions across the pure-applied spectrum, from pure mathematical research, to case studies describing successful application of category-theoretic tools in industry. However, submissions at the most mathematical end should take care to explain how this work could be applied to a subject outside of pure category theory itself, while submissions at the most applied end should contain a clear explanation of the category theory involved.

To accommodate the publishing conventions of different fields, we accept submissions of both original research papers, and also work accepted/submitted/published elsewhere. Accepted original research papers will be invited for publication in a proceedings volume. The keynote addresses will be drawn from the best accepted papers. The conference will include an industry showcase event.


Talks will be given live by speakers, either online or in-person. All talks will be visible by both online and in-person participants. With the permission of the speakers, talks will be made available on YouTube after the conference.

Distinguished Presentation (D)40 minutes
Ordinary Presentation20 minutes
Speaker is in Cambridge (C)

Time (BST) Monday 12 July Tuesday 13 July Wednesday 14 July Thursday 15 July Friday 16 July
0930-1100 Chair: Jamie Vicary (C) Chair: Andrew Pitts (C) Chair: Chris Heunen Chair: Jules Hedges (C) Chair: Richard Blute
WELCOME Konstantinos Meichanetzidis, Robin Lorenz, Anna Pearson, Alexis Toumi, Giovanni de Felice, Dimitri Kartsaklis, Bob Coecke, "QNLP: Compositional Models of Meaning on a Quantum Computer" (D) (s) (v) Emma Chollet, Bryce Clarke, Michael Johnson, Maurine Songa, Vincent Wang, Gioele Zardini, "Limits and colimits in a category of lenses" (D, C) (s) (v) Nicolas Behr, Joachim Kock, "Tracelet Hopf algebras and decomposition spaces" (D) (s) (v) Xiaodong Jia, Bert Lindenhovius, Michael Mislove, Vladimir Zamdzhiev, "Commutative Monads for Probabilistic Programming Languages" (D) (s) (v)
Nihil Shah, "Restricting Power: The Pebble-Relation Comonad in Finite Model Theory" (D, C) (s) (v)
Soichiro Fujii, Yuni Iwamasa, Kei Kimura, "Quantaloidal approach to constraint satisfaction" (s) (v) Matthew Di Meglio, "Coequalisers under the lens" (s) (v) Antonin Delpeuch, Jamie Vicary, "The word problem for braided monoidal categories is unknot-hard" (s) (v) Tobias Fritz, Tomáš Gonda, Paolo Perrone, "De Finetti's Theorem in Categorical Probability" (s) (v)
John van de Wetering, "A categorical construction of the real unit interval" (C) (s) (v) Matt Wilson, Augustin Vanrietvelde, "A categorical framework for the expression of composable constraints: routed categories" (s) (v) Fosco Loregian, Fabrizio Genovese, Daniele Palombi, "A Categorical Semantics for Bounded Petri Nets" (v) Zoltan A. Kocsis, Benjamin Merlin Bumpus, "Treewidth via Spined Categories" (s) (v) Razin A. Shaikh, Lia Yeh, Benjamin Rodatz, Bob Coecke, "Composing Conversational Negation" (C) (s) (v)
1130-1300 Chair: Vladimir Zamdzhiev Chair: Jules Hedges (C) Chair: Ben MacAdam Chair: Bob Coecke Chair: Fabrizio Romano Genovese
Titouan Carette, Marc de Visme, Simon Perdrix, "Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory" (D) (v) Andrew Pitts, S. C. Steenkamp, "Constructing Initial Algebras Using Inflationary Iteration" (D, C) (s) (v) Geoff Cruttwell, Bruno Gavranovic, Neil Ghani, Paul Wilson, Fabio Zanasi, "Categorical Foundations of Gradient-Based Learning" (D, C) (s) (v) Cole Comfort, Aleks Kissinger, "A Graphical Calculus for Lagrangian Relations" (D, C) (s) (v) Chad Nester, "Situated Transition Systems" (s) (v)
Elena Di Lavore, Alessandro Gianola, Mario Román, Nicoletta Sabadini, Pawel Sobocinski, "A Canonical Algebra of Open Transition Systems (Extended Abstract)" (s) (v)
George Kaye, Dan R. Ghica, "Rewriting Graphically with Cartesian Traced Categories" (C) (s) (v) Tomáš Jakl, Anuj Dawar, Luca Reggio, "Lovász-Type Theorems and Game Comonads" (C) (s) (v) Dan Shiebler, Bruno Gavranovic, Paul Wilson, "Category Theory in Machine Learning" (s) (v) Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering, Sal Wolffs, "The ZH-calculus: completeness and extensions" (C) (s) (v) Joe Moeller, "Noncommutative network models" (s) (v)
Paul Wilson, Fabio Zanasi, "The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition" (v) Rowan Poklewski-Koziell, "A note on Frobenius-Eilenberg-Moore objects in dagger 2-categories" (s) (v) Dan Shiebler, "Functorial Manifold Learning" (s) (v) Alexis Toumi, Richie Yeung, Giovanni de Felice, "Diagrammatic Differentiation for Quantum Machine Learning" (v) Gunnar Fløystad, "Profunctors between posets, and Alexander duality" (s) (v)
1400-1530 Chair: David I. Spivak Chair: Dorette Pronk Chair: Geoffrey Cruttwell Chair: Martti Karvonen Chair: Daniel Cicala
Sean Tull, "A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces" (D) (s) (v) Sophie Libkind, Andrew Baas, Evan Patterson, James Fairbanks, "Operadic Modeling of Dynamical Systems: Mathematics and Computation" (D) (s) (v) Matteo Capucci, Neil Ghani, Jérémy Ledent, Fredrik Nordvall Forsberg, "Translating Extensive Form Games to Open Games with Agency" (D, C) (s) (v) Jason Parker, Pieter Hofstra, Philip Scott, "Polymorphic automorphisms and the Picard group" (D) (s) (v) Tslil Clingman, Brendan Fong, David Spivak, "Graphical Regular Logic: the complete 2-dimensional picture" (D) (s) (v)
Toby St Clere Smithe, "Polynomial Life: the Structure of Adaptive Systems" (s) (v) John Foley, Spencer Breiner, Eswaran Subrahmanian, John Dusel, "Operads for complex system design specification, analysis and synthesis" (s) (v) Hans Riess, Paige Randall North, Robert Ghrist, "Network Sheaves Valued in Categories of Adjunctions and their Laplacians" (s) (v) Christian Williams, Michael Stay, "Native Type Theory" (s) (v) Guillaume Boisseau, Pawel Sobocinski, "String Diagrammatic Electrical Circuit Theory" (C) (s) (v)
Matteo Capucci, Bruno Gavranovic, Jules Hedges, Eigil Rischel, "Towards foundations of categorical cybernetics" (C) (s) (v) Jean-Simon Lemay, "Jacobians and Gradients for Cartesian Differential Categories" (s) (v) Jérémie Koenig, "Grounding Game Semantics in Categorical Algebra" (s) (v) Robin Cockett, Priyaa Varshinee Srinivasan, "Exponential modalities and complementarity" (s) (v) Brendan Fong, Alberto Speranzon, David I. Spivak, "Temporal Landscapes: A Graphical Logic of Behavior" (s) (v)
1600-1730 Chair: Jamie Vicary (C) Chair: Brendan Fong Chair: Kohei Kishida Chair: Kohei Kishida Chair: Jade Master
Philip Wadler, University of Edinburgh and IOHK
Brendan Fong, Topos Institute
Jelle Herold, Statebox
Ryan Wisnesky, Conexus
Stelios Tsampas, "Safety for bisimulation for coalgebraic dynamic logic"
Amin Karamlou, Gabriel Goren, "Stochastic game logic, coalgebraically"
Owen Lewis, Elise Catania, Hussain Kadhem, Matthew Di Meglio, "Optimization and profunctor nuclei"
Angeline Aguinaldo, Kris Brown, "Polynomial functors and mode-dependent dynamical systems in Catlab"
Amy Searle, Anna Knorr, Grant Generaux, "Computing Ising models graphically - DPO for Markov Chains"
Emma Phillips, Claire Ott, Elise McMahon, "Weakly globular double categories and Petri nets"
POSTER SESSION Alexis Toumi, Alex Koziell-Pipe, "Functorial Language Models" (s) (v) Michael Lambert, "Characterizing Double Categories of Relations" (s) (v)
DRINKS RECEPTION Lachlan McPheat, Gijs Wijnholds, Mehrnoosh Sadrzadeh, Adriana Correia, Alexis Toumi, "Anaphora and Ellipsis in Lambek Calculus with a Relevant Modality: Syntax and Semantics" (C) (s) (v) Victoria Noquez, Larry Moss, "The Sierpinski Carpet as a Final Coalgebra" (s) (v)
David Spivak, "Learners' languages" (s) (v) Anne Broadbent, Martti Karvonen, "Categorical composable cryptography" (s) (v)

Conference Photo

Left-to-right (with a front-to-back sublist): Tomas Jakl, Nick Hu, Nihil Shah, Hao Xu, Ieva Cepaite, Amin Karamlou, Amy Searle, Jules Hedges, Callum Reader, Benjamin Rodatz, Bruno Gavranovic, Swaraj Dash, (Razin Shaikh, Zanzi Mihejevs, Dylan Braithwaite, Joseph Grant), Joseph Martin, Paul Wilson, Cole Comfort, Matteo Capucci, Alex Rice, Calin Tataru, Simon Willerton, Ioannis Markakis, George Kaye, Robert Furber, and Lukas Heidemann.

Accepted Presentations

The following 51 submissions have been accepted for presentation at ACT 2021. A full programme is available below. The suffix "(D)" indicates the submission has been selected for a distinguished presentation, while the suffix "(C)" denotes that it will be presented in person in Cambridge. The submissions are ordered according to their original submission number.

Accepted Posters

The following posters will be presented at the poster presentation session on Wednesday afternoon, in the form of lightning talks of a single slide. Italics indicate the person presenting the poster.

  • Abel Sagodi, "Conceptualizing explanations through category theory" (poster)
  • Owen Lynch, James Fairbanks and Evan Patterson, "Graphical Semantic Modeling with Semagrams.jl"
  • Henry Kvinge, Brett Jefferson, Cliff Joslyn and Emilie Purvine, "Sheaves as a Framework for Understanding and Interpreting Model Fit" (poster)
  • Maria Dimarogkona, Mark Addis and Petros Stefaneas, "Syntax, Semantics and the Formalisation of Social Science Theories" (poster)
  • Davide Trotta, Matteo Spadetto and Valeria de Paiva, "The Gödel fibration" (poster)
  • Tim Hosgood and David I. Spivak, "Dirichlet polynomials and entropy" (poster)
  • Daniel Luckhardt and Matt Insall, "Norms on Categories" (poster)
  • Elena Di Lavore, Wilmer Leal and Valeria de Paiva, "Dialectica Petri nets" (poster)
  • Jonas Frey and Colin Zwanziger, "Elementary (1,2)-cosmoses and labeled linear logic" (poster)
  • Joshua Tan and Aleksandar Petrov, "A type system of digital institutions" (poster)

Important Dates

All dates are in 2021, and all deadlines are Anywhere-on-Earth on the given date.

  • Submission Deadline: Monday 10 May Wednesday 12 May
  • Author Notification: Monday 7 June
  • Financial Support Application Deadline: Monday 7 June Tuesday 8 June
  • Financial Support Notification: Tuesday 8 June Wednesday 9 June
  • Priority Physical Registration Opens: Wednesday 9 June
  • Ordinary Physical Registration Opens: Friday 11 June
  • Adjoint School: Monday 5 to Friday 9 July
  • Main Conference: Monday 12 to Friday 16 July


The organizers are committed to ensuring a fantastic experience for both online and in-person participants. If you are giving a presentation at ACT 2021, you can do this either online or in-person.

Online participation. Online participation has now closed.

Physical participation. Registration for physical participation is now closed. If you do not have a registration, please do not show up in person at the conference. Due to the need for physical distancing the number of tickets has been precisely controlled.

Information for Participants

Online participation will be via Zoom. If you want to participate online, please make sure to register (see Registration section above.)

Current UK government projections indicate that physical conference participation will be allowed for the conference dates. However, there of course remains a possibility that circumstances may change, and the organizers may reluctantly decide to cancel the physical confence due to circumstances related to the pandemic. If the physical conference is cancelled, any money paid for registration would be refunded. However, the organizers will not be liable for any other costs that physical participants may have, such as travel or accommodation. If you are not willing to take this risk, we suggest you plan to participate online.

The physical conference will take place at the Computer Laboratory (also known as the Department of Computer Science and Technology) at the University of Cambridge, shown on the following map. The department is situated about 1.5 miles to the west of the city, and it takes about 30 minutes to walk there from the city centre. Buses can be unreliable, so walking or cycling is the usual mode of transport around the city; there are plenty of cycle hire places that can be found on Google Maps. If you need a taxi, Uber operates in the city, and Camcab is a traditional taxi firm which can be contacted on 01223 704704. There is a nice cycle path which is an ideal way to walk or cycle between the department and the city centre, illustrated on the map below.

Accommodation in Cambridge can be booked through the usual websites. In particular we recommend as a source of good-value accommodation, and suggest Fitzwilliam College as a low-priced option which is conveniently located close to both the conference location and the city centre.

Internet access is available at the conference venue through the Eduroam service. The best way to set this up is by using the Eduroam configuration tool, available for a wide range of devices.

The physical conference will be organized in a COVID-safe way. In particular, participants will be expected to observe social distancing, the number of participants will be restricted, seating in the lecture theatre will be well-spaced, coffee and lunch breaks will be outdoors where possible, and masks will be required while not eating or drinking, including for in-person speakers during their lecture.

Here is a list of food options that you can try while you are here:

  • Pubs

    • THE EAGLE, 8 Benet Street
    • THE PICKEREL Inn, 30 Magdalen Street
    • THE ARCHITECT, 43 Castle Street
    • THE GRAIN & HOP STORE, Regent Terrace
  • Restaurants

    • LITTLE PETRA, 94 Mill Road
    • LITTLE SEOUL, 108 Regent Street
    • THE OLIVE GROVE, 100 Regent Street
    • PHO, 1 Wheeler Street
    • FRANCO MANCA, 15 Market Hill
  • Fast Food

    • TORTILLA, 18 Market Passage
    • AROMI, 1 Benet Street
    • WASABI, One Station Square
    • MADINGLEY ROAD KEBAB, 1 Madingley Road

Financial Support

Financial support applications have now closed.

Some financial support is available to support attendance by junior researchers who would like to attend the conference in person. To apply for this, send an email to Lukas Heidemann at from an academic email address, with subject line "ACT 2021 Financial Support Application".

In your email, please give the following information: your name and affiliation; an estimate of the total cost for you to attend; the amount you are requesting; whether or not you have had a paper accepted to the conference (and if so, its submission number); and whether you have secured or applied for partial funding from another source (if so, this will strengthen your application). Also, please give a brief statement about why you believe that COVID restrictions will not prevent you from attending (e.g. "I live in the UK, and current government projections indicate no restrictions on conference travel and participation in July".)

You will be informed about the result of your application on Tuesday 8 June Wednesday 9 June. Successful applicants for financial support will be eligible for the Priority Physical Registration period, which opens on Wednesday 9 June.


Submission via EasyChair is now closed.

There are two submission tracks, both of which will be reviewed against the same standards of quality. Submission of work-in-progress is encouraged, but it must be more substantial than a research proposal.

  • Proceedings Track. Original contributions of high-quality work consisting of an extended summary, up to 12 pages excluding bibliography, that provides evidence of results of genuine interest, and with enough detail to allow the program committee to assess the merits of the work. Full proofs of mathematical statements are not necessarily required. Accepted submissions in this track will be invited for publication in a proceedings volume. Submissions to this track must be prepared with LaTeX, using the EPTCS style files available at Additional appendices beyond the page limit are permitted but may not be read by reviewers, and will not be included in the proceedings.
  • Non-Proceedings Track. Submissions presenting high-quality work submitted or published elsewhere, or for which publication in the proceedings is not desired by the authors, may be submitted to this track, provided the work is recent and relevant to the conference. The work may be of any length, but the program committee members may only look at the first 3 pages of the submission, so you should ensure that these pages contain sufficient evidence of the quality and rigour of your work.

Since ACT is an interdisciplinary conference, we use two tracks to accommodate the publishing conventions of different disciplines. For example, those from a Computer Science background may prefer the Proceedings Track, while those from a Mathematics, Physics or other background may prefer the Non-Proceedings Track. However, authors from any background are free to choose the track that they prefer, and submissions may be moved from the Proceedings Track to the Non-Proceedings Track at any time at the request of the authors.

Adjoint School

Applications for the Adjoint School 2021 are now closed.

The Adjoint School is an annual collaborative research event, in which junior researchers work on cutting-edge topics in applied category theory, guided by expert mentors. Traditionally, after a four month reading course, the participants meet at the venue of the ACT conference for a week of in-person research collaborator. Due to the pandemic, this year the research week will be held online. The students will share the results of their research in a special session during the ACT conference.

For more information see the official school website.

Statement of Values

The organizers hope that the Applied Category Theory community can be a positive force in the world. To help us achieve this, we have drafted a Statement of Values, which we ask all participants to uphold.


Programme Committee

Local Organizers

Lukas Heidemann
University of Oxford

Nick Hu
University of Oxford

Ioannis Markakis
University of Cambridge

Alex Rice
University of Cambridge

Calin Tataru
University of Cambridge

Jamie Vicary
University of Cambridge

Steering Committee

  • John Baez, University of California Riverside and Centre for Quantum Technologies
  • Bob Coecke, Cambridge Quantum Computing
  • Dorette Pronk, Dalhousie University
  • David Spivak, Topos Institute