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

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.

We hope to run the conference as a hybrid event, with physical attendees present in Cambridge, and other participants taking part online. However, due to the state of the pandemic, the possibility of in-person attendance is not yet confirmed. Please do not book your travel or hotel accommodation yet.

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

  • Submission Deadline: Monday 10 May 2021
  • Author Notification: Monday 7 June 2021
  • Registration: TBD
  • Adjoint School: Monday 5 to Friday 9 July 2021
  • Main Conference: Monday 12 to Friday 16 July 2021


Submission will be via EasyChair, and is not yet open.

Two types of submissions are accepted, both of which will be reviewed using the same standards:

  • Proceedings Track. Original contributions of high-quality work consisting of an extended abstract, up to 12 pages, that provides evidence of results of genuine interest, and with enough detail to allow the program committee to assess the merits of the work. Submission of work-in-progress is encouraged, but it must be more substantial than a research proposal. Accepted submissions in this track will be invited for publication in a proceedings volume.
  • 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.

Papers in the two tracks will be reviewed against the same standards of quality. 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.

Contributions must be submitted in PDF format. Submissions to the Proceedings Track must be prepared with LaTeX, using the EPTCS style files available at


The scientific programme is not yet available.

Local Information

To be announced.


To be announced.

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

The programme committee will be announced soon.

Local Organizers

Lukas Heidemann
University of Oxford

Nick Hu
University of Oxford

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
  • David Spivak, Topos Institute