Bryce Clarke

email: bryce.clarke@taltech.ee

google scholar: link | arXiv: link | CV: link

pronouns: he / him

I am a postdoctoral researcher at the Tallinn University of Technology in Tallinn, Estonia. I am a member of the Logic and Semantics Group led by Tarmo Uustalu.

Before that, I was a postdoctoral researcher for two years at Inria Saclay in Palaiseau, France. There I worked with Gabriel Scherer and Noam Zeilberger in the PARTOUT team.

I completed my PhD with Michael Johnson at the Centre of Australian Category Theory (CoACT) at Macquarie University in Sydney, Australia.

I am broadly interested in category theory and its applications, and so far my research has focused on lenses, (op)fibrations, cofunctors, double categories, and factorisation systems.

Recent news

Together with Dorette Pronk, Marco Grandis, and Christina Vasilakopoulou, I am a guest editor the Collection honouring Robert Paré for his 80th birthday in Applied Categorical Structures.
Submissions are now open from 1 October 2024 until 30 June 2025 - please consider submitting your work!

Together with Tim Hosgood, I organised the Second Virtual Workshop on Double Categories, held online via Zoom between 21-30 October 2024. The recordings and slides are now available!

I have a new paper on the arXiv in February 2025 on The Grothendieck construction for delta lenses.

Nathanael Arkor recently delivered a talk on our joint work at the Topos Colloquium titled A (virtual) double category theorist's perspective on polynomials. Check out the recording and slides!

Upcoming travel

I will also be speaking about A new framework for limits in double categories at the International Category Theory Conference 2025 in Brno, Czech Republic from 13-19 July 2025.

Research papers

Publications

1. Lifting twisted coreflections against delta lenses
   Theory and Applications of Categories, Vol. 41, No. 26, 2024, pp. 838-877. (pdf)
2. Profunctor optics: a categorical update
   (with Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, and Mario Román)
   Compositionality, Vol. 6, No. 1, 2024. (pdf)
3. The algebraic weak factorisation system for delta lenses
   Proceedings of the Sixth International Conference on Applied Category Theory 2023,
   Electronic Proceedings in Theoretical Computer Science, Vol. 397, 2023, pp. 54-69. (pdf)
4. Limits and colimits in a category of lenses
   (with Emma Chollet, Michael Johnson, Maurine Songa, Vincent Wang, and Gioele Zardini)
   Proceedings of the Fourth International Conference on Applied Category Theory,
   Electronic Proceedings in Theoretical Computer Science, Vol. 372, 2022, pp. 164-177. (pdf)
5. Delta lenses as coalgebras for a comonad
   STAF 2021 Workshop Proceedings: 9th International Workshop on Bidirectional Transformations,
   CEUR Workshop Proceedings, Vol. 2999, 2021, pp. 18-27. (pdf)
6. A diagrammatic approach to symmetric lenses
   Proceedings of the 3rd Annual International Applied Category Theory Conference 2020,
   Electronic Proceedings in Theoretical Computer Science, Vol. 333, 2021, pp. 79-91. (pdf)
7. Internal split opfibrations and cofunctors
   Theory and Applications of Categories, Vol. 35, No. 44, 2020, pp. 1608-1633. (pdf)
8. Internal lenses as functors and cofunctors
   Proceedings Applied Category Theory 2019,
   Electronic Proceedings in Theoretical Computer Science, Vol. 323, 2020, pp. 183-195. (pdf)

Preprints

• The Grothendieck construction for delta lenses
  arXiv:2502.21288, 41 pages. (pdf)
• An introduction to enriched cofunctors
  (with Matthew Di Meglio)
  arXiv:2209.01144, 16 pages. (pdf)

Other writing

• The double category of lenses
  PhD thesis, Macquarie University, February 2022. (pdf)
• Characterising asymmetric lenses using internal categories
  Master's thesis, Macquarie University, December 2018. (pdf)

Research talks

Conferences and workshops

• Understanding delta lenses using category theory, Bidirectional Transformations: Foundations and Applications, NII Shonan Meeting, Japan, 26 - 29 May 2025. (slides)
• The algebraic weak factorisation system of twisted coreflections and delta lenses, International Category Theory Conference (CT2024), University of Santiago de Compostela, 23 to 29 June 2024. (slides, abstract)
• The Grothendieck construction for delta lenses, Applied Category Theory Conference (ACT2024), University of Oxford, 17 to 21 June 2024. (slides, extended abstract)
• The algebraic weak factorisation system for delta lenses - Applied Category Theory Conference (ACT2023), University of Maryland, 31 July to 4 August 2023. (slides, video)
• The right-connected completion of a double category - International Category Theory Conference (CT2023), UCLouvain, 2 to 8 July 2023. (slides, abstract)
• Lifting and lenses - LHC days 2023, IRIF, Université Paris Cité, 6 June 2023. (slides)
• Enriched lenses - Applied Category Theory Conference (ACT2022), University of Strathclyde and online, 18 to 22 July 2022. (slides, extended abstract, video)
• Three approaches to lenses over a base - International Category Theory Conference (CT20→21), University of Genoa and online, 30 August to 4 September 2021. (slides, abstract, video)
• Delta lenses as coalgebras for a comonad - Ninth International Workshop on Bidirectional Transformations (Bx2021), Western Norway University of Applied Sciences (online), 21 June 2021. (slides)
• Cofunctors, lenses, and split opfibrations - Workshop on Polynomial Functors, Topos Institute (online), 15 to 19 March 2021. (slides, video)
• Generalising fibrations via multi-valued functions - 64th Annual Meeting of the Australian Mathematical Society (AustMS2020), University of New England (online), 8 to 11 December 2020. (slides)
• A diagrammatic approach to symmetric lenses - Applied Category Theory Conference (ACT2020), Massachusetts Institute of Technology (online), 6 to 10 July 2020. (slides, video)
• Characterising split opfibrations using lenses - 63rd Annual Meeting of the Australian Mathematical Society (AustMS2019), Monash University, 3 to 6 December 2019. (slides)
• Internal lenses as functors and cofunctors - Applied Category Theory Conference (ACT2019), University of Oxford, 15 to 19 July 2019. (slides, video)
• Internal lenses as monad morphisms - International Category Theory Conference (CT2019), University of Edinburgh, 7 to 13 July 2019. (slides, abstract)
• Split opfibrations and cofunctors - 27th Foundational Methods in Computer Science Workshop (FMCS2019), University of Calgary, 28 May to 2 June 2019.

Seminars and Colloquia

• The free split opfibration on a delta lens - Computer Science Theory Seminar, Tallinn University of Technology, 24 April 2025. (slides)
• Limits and colimits in double categories by example (expository talk) - Junior Category Theory Seminar, UCLouvain, 9 October 2024. (notes)
• Reflecting on lenses and split opfibrations - Edinburgh Category Theory Seminar, University of Edinburgh (online), 2 October 2024. (slides)
• A new perspective on comodules of polynomial comonads - Computer Science Theory Seminar, Tallinn University of Technology, 30 May 2024. (notes)
• The AWFS of twisted coreflections and delta lenses - Category Theory Seminar, UCLouvain, 4 December 2023. (slides)
• Lifting twisted coreflections against delta lenses - Computer Science Theory Seminar, Tallinn University of Technology, 9 November 2023. (slides)
• Reflections on delta lenses - Chocola, ENS Lyon, 15 June 2023. (slides)
• The right-connected completion of a double category - Higher categories, polygraphs and homotopy working group, IRIF, Université Paris Cité, 17 February 2023. (slides)
• Algebraic weak factorisation systems (expository talk) - Junior Category Theory Seminar, UCLouvain, 7 November 2022.
• A double-categorical approach to lenses via algebraic weak factorisation systems - Topos Institute Colloquium, Topos Institute (online), 3 November 2022. (slides, video)
• Basic concepts of enriched cofunctors - Masaryk University Algebra Seminar, Masaryk University, 27 October 2022.
• An introduction to enriched cofunctors - Theoretical Cosynus Seminar, Inria Saclay / LIX, 6 October 2022. (slides)
• Investigating lenses between preordered sets - Proofs and Algorithms Seminar, Inria Saclay / LIX (online), 20 June 2022. (slides)
• An introduction to delta lenses - Theoretical Cosynus Seminar, Inria Saclay / LIX, 18 May 2022. (slides)
• Constructing lenses in double categories - Intercats Seminar, Topos Institute (online), 19 April 2022. (slides, video)
• A general framework for cofunctors - Computer Science Theory Seminar, Tallinn University of Technology (online), 7 April 2022. (slides, video)
• The Grothendieck construction for lenses - The Calgary Peripatetic Seminar, University of Calgary (online), 26 March 2021. (slides)

Australian Category Seminar

Here is a list of my talks at the Australian Category Seminar.

• The right-connected completion - 29 June 2022. (slides)
• Enriched lenses - 27 October 2021. (slides)
• The double category of generalised lenses - 22 September 2021. (slides)
• Lenses as coalgebras for a comonad - 28 April 2021. (slides)
• What's so nice about the category of lenses? - 17 February 2021. (slides)
• Cofunctors, monoids, and split epimorphisms - 28 October 2020. (slides)
• Lax double functors into Span-like double categories - 30 September 2020. (slides)
• Lenses as algebras for a monad - 26 August 2020. (slides)
• Internal split opfibrations, lenses, and decalage - 27 November 2019.
• Symmetric lenses as Mealy morphisms - 21 August and 25 September 2019.
• Internal lenses - 21 November 2018.

Academic activities

• Guest Editor - Collection honouring Robert Paré for his 80th birthday, Applied Categorical Structures, submissions open 1 October 2024 - 30 June 2025.
• Co-organiser - The Second Virtual Workshop on Double Categories, to be held online from 21-30 October 2024.
• Program Committee - Applied Category Theory 2024 conference, University of Oxford.
• Program Committee - Applied Category Theory 2023 conference, University of Maryland.
• Program Chair and Local Organiser - Eleventh Symposium on Compositional Structures, held at École Polytechnique from 20 to 21 April 2023.
• Co-organiser - Virtual Double Categories Workshop, held online from 28 November to 2 December 2022.
• Program Committee - Applied Category Theory 2022 conference, University of Strathclyde.
• Organiser - Australian Category Seminar, Macquarie University, August to December 2021.
• Scientific Committee - Australian Kittens 2021: A Meeting of Early Career Researchers in Category Theory and Homotopy Theory, held online from 2 to 3 December 2021.
• Co-organiser - Categories and Companions Symposium, held online from 8 to 12 June 2021.
• Teaching Assistant - Applied Category Theory 2020 Adjoint School, Categories of Maintainable Relations project, held at Massachusetts Institute of Technology (online), 29 June to 3 July 2020.
• Participant - Applied Category Theory 2019 Adjoint School, Traversal Optics and Profunctors project, held at University of Oxford, 22 to 26 July 2019.

Other links

• Categories mailing list - The international category theory mailing list.
• Theory and Applications of Categories - An open-access journal on category theory, categorical methods and their applications in the mathematical sciences.
• Cahiers de Topologie et Géométrie Différentielle Catégoriques - An open-access journal on pure category theory and its applications.
• Higher Structures - An open-access journal on the theory of higher structures and its applications in the mathematical sciences.
• Compositionality - An open-access journal for the mathematics of composition.
• arXiv [math.CT] - Recent preprints in category theory on the arXiv.
• The Adjoint School - An annual research school in applied category theory.
• Topos Institute - An applied category theory research institute.
• MSC 2020 - Mathematics Subject Classification System.
• nLab - A collaborative category theory wiki.
• Pentolla - An online platform for the abstract strategy board game Blokus.