Bryce Clarke

email: bryce.clarke1@hdr.mq.edu.au

I am a PhD student, supervised by Emeritus Professor Michael Johnson and Emeritus Professor Dominic Verity.

I am a member of the Centre of Australian Category Theory (CoACT) and the Department of Mathematics and Statistics at Macquarie University, Sydney, Australia.

I am interested in category theory, and my current research focuses on lenses, opfibrations, and cofunctors.

Research papers

Publications

1. Delta lenses as coalgebras for a comonad, in Proceedings Bx 2021, CEUR Workshop Proceedings 2999 (2021), 18--27.
2. A diagrammatic approach to symmetric lenses, in Proceedings ACT 2020, Electronic Proceedings in Theoretical Computer Science 333 (2021), 79--91.
3. Internal split opfibrations and cofunctors, Theory and Applications of Categories 35 (2020), 1608--1633.
4. Internal lenses as functors and cofunctors, in Proceedings ACT 2019, Electronic Proceedings in Theoretical Computer Science 323 (2020), 183--195.

Preprints

• Limits and colimits in a category of lenses (with Emma Chollet, Michael Johnson, Maurine Songa, Vincent Wang, Gioele Zardini), May 2021, accepted for the proceedings of ACT2021.
• Profunctor optics, a categorical update (with Derek Elkins, Jeremy Gibbons, Fosco Loregian, Bartosz Milewski, Emily Pillmore, Mario Román), January 2020, preprint.

Research talks

Conferences and workshops

• 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, 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)
• The Grothendieck construction for lenses - The Calgary Peripatetic Seminar, University of Calgary (online), 26 March 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.

Australian Category Seminar

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

• 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.
• Lax double functors into Span-like double categories - 30 September 2020.
• Lenses as algebras for a monad - 26 August 2020.
• 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

• Organiser - Australian Category Seminar, Macquarie University, current.
• Scientific Committee - Australian Kittens 2021: A Meeting of Early Career Researchers in Category Theory and Homotopy Theory, to be 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.