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.

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


You may register for either online or in-person attendance. 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. Registration for online participation is free, and is now open at the following link. Registering for online participation does not prevent you registering at a later date for physical participation if you would like to do that.

Physical participation. A limited number of registrations for in-person attendance are currently available to purchase from the following link, at a cost of £110:

As part of the purchase process, you are asked why you believe you will not be prevented to travel to the conference due to COVID restrictions. Examples of acceptable responses include: that you are currently in the UK or its Common Travel Area (Ireland, the Channel Islands and the Isle of Man); that you are in a green list country allowing quarantine-free travel to the UK; or that you are in an amber list country, and will travel to the UK in sufficient time to complete the mandatory 10-day quarantine before the start of the conference. If you are not able to give an acceptable answer to this question, your registration will be cancelled and refunded. If you have any questions about this policy, feel free to contact one of the local organizers.

Local Information

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, as well as any money paid for the official conference accommodation at King's College. However, the organizers will not be liable for any other costs that physical participants may have, such as travel, or accommodation that has been separately arranged. If you are not willing to take this risk, we suggest you plan to participate online.

The physical conference will take place at the Department of Computer Science at the University of Cambridge. Information about travel will follow soon.

For those with a confirmed in-person registration, the official conference accommodation at King's College can be purchased via the following link for £474, with check-in on Monday 12 July and check-out on Friday 16 July. We have arranged with King's College that the accommodation fee will be refunded if the conference is cancelled by the organizers due to the pandemic. King's College is situated in Cambridge town centre, and is a 30-minute walk to the conference venue. This booking includes breakfast at King's College on Tuesday, Wednesday and Thursday morning, but not Friday morning.

Alternatively, you may arrange your own accommodation in Cambridge, which 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.

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.

Accepted Presentations

The following 50 submissions have been accepted for presentation at ACT 2021. A full programme will be available closer to the conference dates. The suffix "(D)" indicates the submission has been selected for a distinguished presentation. The submissions are ordered according to their original submission number.

  • Dan Shiebler, "Functorial Manifold Learning"
  • David Spivak, "Learners' languages"
  • Jean-Simon Lemay, "Jacobians and Gradients for Cartesian Differential Categories"
  • John van de Wetering, "A categorical construction of the real unit interval"
  • Miriam Backens, Aleks Kissinger, Hector Miller-Bakewell, John van de Wetering and Sal Wolffs, "The ZH-calculus: completeness and extensions"
  • Fosco Loregian, Fabrizio Genovese and Daniele Palombi, "A Categorical Semantics for Bounded Petri Nets"
  • Rowan Poklewski-Koziell, "A note on Frobenius-Eilenberg-Moore objects in dagger 2-categories"
  • Geoff Cruttwell, Bruno Gavranovic, Neil Ghani, Paul Wilson and Fabio Zanasi, "Categorical Foundations of Gradient-Based Learning" (D)
  • Anne Broadbent and Martti Karvonen, "Categorical composable cryptography"
  • Antonin Delpeuch and Jamie Vicary, "The word problem for braided monoidal categories is unknot-hard"
  • Dan Shiebler, Bruno Gavranovic and Paul Wilson, "Category Theory in Machine Learning"
  • Andrew Pitts and S. C. Steenkamp, "Constructing Initial Algebras Using Inflationary Iteration" (D)
  • Chad Nester, "Situated Transition Systems"
  • Xiaodong Jia, Bert Lindenhovius, Michael Mislove and Vladimir Zamdzhiev, "Commutative Monads for Probabilistic Programming Languages" (D)
  • Christian Williams and Michael Stay, "Native Type Theory"
  • Tobias Fritz, Tomas Gonda and Paolo Perrone, "De Finetti's Theorem in Categorical Probability"
  • Elena Di Lavore, Alessandro Gianola, Mario Román, Nicoletta Sabadini and Pawel Sobocinski, "A Canonical Algebra of Open Transition Systems (Extended Abstract)"
  • Zoltan A. Kocsis and Benjamin Merlin Bumpus, "Treewidth via Spined Categories"
  • John Foley, Spencer Breiner, Eswaran Subrahmanian and John Dusel, "Operads for complex system design specification, analysis and synthesis"
  • Toby St Clere Smithe, "Polynomial Life: the Structure of Adaptive Systems"
  • Matthew Di Meglio, "Coequalisers under the lens"
  • Emma Chollet, Bryce Clarke, Michael Johnson, Maurine Songa, Vincent Wang and Gioele Zardini, "Limits and colimits in a category of lenses" (D)
  • Titouan Carette, Marc de Visme and Simon Perdrix, "Graphical Language with Delayed Trace: Picturing Quantum Computing with Finite Memory" (D)
  • Konstantinos Meichanetzidis, Robin Lorenz, Anna Pearson, Alexis Toumi, Giovanni de Felice, Dimitri Kartsaklis and Bob Coecke, "QNLP: Compositional Models of Meaning on a Quantum Computer" (D)
  • Nihil Shah, "Restricting Power: The Pebble-Relation Comonad in Finite Model Theory" (D)
  • Gunnar Fløystad, "Profunctors between posets, and Alexander duality"
  • Lachlan McPheat, Gijs Wijnholds, Mehrnoosh Sadrzadeh, Adriana Correia and Alexis Toumi, "Anaphora and Ellipsis in Lambek Calculus with a Relevant Modality: Syntax and Semantics"
  • Alexis Toumi, Richie Yeung and Giovanni de Felice, "Diagrammatic Differentiation for Quantum Machine Learning"
  • Alexis Toumi and Alex Koziell-Pipe, "Functorial Language Models"
  • Tslil Clingman, Brendan Fong and David Spivak, "Graphical Regular Logic: the complete 2-dimensional picture" (D)
  • Tomas Jakl, Anuj Dawar and Luca Reggio, "Lovasz-Type Theorems and Game Comonads"
  • Jason Parker, Pieter Hofstra and Philip Scott, "Polymorphic automorphisms and the Picard group" (D)
  • Joe Moeller, "Noncommutative network models"
  • Guillaume Boisseau and Pawel Sobocinski, "String Diagrammatic Electrical Circuit Theory"
  • Sophie Libkind, Andrew Baas, Evan Patterson and James Fairbanks, "Operadic Modeling of Dynamical Systems: Mathematics and Computation" (D)
  • Robin Cockett and Priyaa Varshinee Srinivasan, "Exponential modalities and complementarity"
  • Matteo Capucci, Neil Ghani, Jeremy Ledent and Fredrik Nordvall Forsberg, "Translating Extensive Form Games to Open Games with Agency" (D)
  • Matteo Capucci, Bruno Gavranovic, Jules Hedges and Eigil Rischel, "Towards foundations of categorical cybernetics"
  • Victoria Noquez and Larry Moss, "The Sierpinski Carpet as a Final Coalgebra"
  • George Kaye and Dan R. Ghica, "Rewriting Graphically with Cartesian Traced Categories"
  • Paul Wilson and Fabio Zanasi, "The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition"
  • Brendan Fong, Alberto Speranzon and David I. Spivak, "Temporal Landscapes: A Graphical Logic of Behavior"
  • Hans Riess, Paige Randall North and Robert Ghrist, "Network Sheaves Valued in Categories of Adjunctions and their Laplacians"
  • Michael Lambert, "Characterizing Double Categories of Relations"
  • Soichiro Fujii, Yuni Iwamasa and Kei Kimura, "Quantaloidal approach to constraint satisfaction"
  • Sean Tull, "A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces" (D)
  • Nicolas Behr and Joachim Kock, "Tracelet Hopf algebras and decomposition spaces" (D)
  • Cole Comfort and Aleks Kissinger, "A Graphical Calculus for Lagrangian Relations" (D)
  • Matt Wilson and Augustin Vanrietvelde, "A categorical framework for the expression of composable constraints: routed categories"
  • Razin A. Shaikh, Lia Yeh, Benjamin Rodatz and Bob Coecke, "Composing Conversational Negation"
  • Jeremie Koenig, "Grounding Game Semantics in Categorical Algebra"


There will be a single track of talks, given live by speakers, either online or in-person. All talks will be visible by both online and in-person participants. The scientific programme is not yet available.

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