Bryce Clarke

email: bryce.clarke@inria.fr

google scholar: link | arXiv: link | twitter: link | mathstodon: link

pronouns: he / him

I am a postdoctoral researcher at the Inria Saclay Centre in Palaiseau, France, where I am working with Gabriel Scherer and Noam Zeilberger in the PARTOUT team.

Before that, I was a PhD student at the Centre of Australian Category Theory (CoACT) and 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, and double categories.

Recent news

• 2022-11-28 → 2022-12-02: I am organising the Virtual Double Categories Workshop with Tim Hosgood.
• 2022-11-03: My joint paper Limits and colimits in a category of lenses was published in the Proceedings of ACT2021.
• 2022-11-03: I delivered a talk titled A double-categorical approach to lenses via algebraic weak factorisation systems at the Topos Institute Colloquium.
• 2022-10-24 → 2022-10-28: I visited John Bourke at Masaryk Univerisity in Brno, Czech Republic.
• 2022-10-12 → 2022-10-13: I attended Journées LHC 2022 at ENS Paris Saclay in France.
• 2022-10-06: I delivered a talk titled An introduction to enriched cofunctors at the Theoretical Cosynus Seminar.
• 2022-09-06 → 2022-09-09: I attended the Chaire de la Vallée Poussin 2022 lectures and the Workshop on Categories and Topology at UCLouvain in Louvain-la-Neuve, Belgium.
• 2022-09-02: I have a new preprint on the arXiv titled An introduction to enriched cofunctors with Matthew Di Meglio.

Research papers

Publications

1. Limits and colimits in a category of lenses (with Emma Chollet, Michael Johnson, Maurine Songa, Vincent Wang, Gioele Zardini), in Proceedings ACT 2021, EPTCS 372 (2022), 164--177.
2. Delta lenses as coalgebras for a comonad, in Proceedings Bx 2021, CEUR Workshop Proceedings 2999 (2021), 18--27.
3. A diagrammatic approach to symmetric lenses, in Proceedings ACT 2020, EPTCS 333 (2021), 79--91.
4. Internal split opfibrations and cofunctors, Theory and Applications of Categories 35 (2020), 1608--1633.
5. Internal lenses as functors and cofunctors, in Proceedings ACT 2019, EPTCS 323 (2020), 183--195.

Preprints

• An introduction to enriched cofunctors (with Matthew Di Meglio), September 2022, preprint.
• Profunctor optics, a categorical update (with Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, Mario Román), January 2020, preprint.

Other writing

• The double category of lenses, PhD thesis, Macquarie University, February 2022. Supervisors: Michael Johnson and Dominic Verity.
• Characterising asymmetric lenses using internal categories, Master's thesis, Macquarie University, December 2018. Supervisor: Michael Johnson.

Research talks

Conferences and workshops

• Enriched lenses - Applied Catgeory Theory Conference (ACT2022), University of Strathclyde and online, 18 July to 22 July 2022. (extended abstract, video, slides)
• Three approaches to lenses over a base - International Category Theory Conference (CT20→21), University of Genoa and online, 30 August to 4 September 2021. (abstract, video, slides)
• 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 March to 19 March 2021. (video, slides)
• Generalising fibrations via multi-valued functions - 64th Annual Meeting of the Australian Mathematical Society (AustMS2020), University of New England (online), 8 December to 11 December 2020. (slides)
• A diagrammatic approach to symmetric lenses - Applied Category Theory Conference (ACT2020), Massachusetts Institute of Technology (online), 6 July to 10 July 2020. (video, slides)
• Characterising split opfibrations using lenses - 63rd Annual Meeting of the Australian Mathematical Society (AustMS2019), Monash University, 3 December to 6 December 2019. (slides)
• Internal lenses as functors and cofunctors - Applied Category Theory Conference (ACT2019), University of Oxford, 15 July to 19 July 2019. (video, slides)
• Internal lenses as monad morphisms - International Category Theory Conference (CT2019), University of Edinburgh, 7 July to 13 July 2019. (abstract, slides)
• Split opfibrations and cofunctors - 27th Foundational Methods in Computer Science Workshop (FMCS2019), University of Calgary, 28 May to 2 June 2019.

Seminars and Colloquia

• 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. (video, slides)
• 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. (video, slides)
• A general framework for cofunctors - Computer Science Theory Seminar, Tallinn University of Technology (online), 7 April 2022. (video, slides)
• 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

• Co-organiser - Virtual Double Categories Workshop, to be 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 December to 3 December 2021.
• Co-organiser - Categories and Companions Symposium, held online from 8 June 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 July to 26 July 2019.

Other links

• Category theory resources - A collection of books, papers, and resources on various topics in category theory.
• 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.