Matthew Di Meglio

About

I am a PhD student in the Laboratory for Foundations of Computer Science at the University of Edinburgh working with Chris Heunen and Perdita Stevens.

I am interested in applied category theory, especially applications of category theory to computer science. My current work relates to dagger categories and Hilbert spaces, with loose connections to quantum computing. My previous work focused on delta lenses—a category theoretic model of bidirectional transformations, polynomial functors and indexed categories.

Publications

  • Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
    (with Chris Heunen)
    Applied Categorical Structures, 2025.
    [DOI, arXiv]
  • Universal Properties of Lens Proxy Pullbacks
    Applied Category Theory 2022.
    [DOI, GitHub, Video, Handout]
  • The category of asymmetric lenses and its proxy pullbacks
    Master of Research thesis, Macquarie University, 2021.
    [DOI, GitHub]
  • Coequalisers under the lens
    Applied Category Theory 2021.
    [DOI, GitHub, Video, Handout]
  • Chebotarev's density theorem
    Honours thesis, UNSW Sydney, 2019.
    [GitHub]

Preprints

  • M*-categories: Where limits in analysis and category theory meet
    (with Chris Heunen)
    [arXiv]
  • R*-categories: The Hilbert-space analogue of abelian categories
    [arXiv]
  • An introduction to enriched cofunctors
    (with Bryce Clarke)
    [arXiv, GitHub]

Talks

  • Dagger Categories of Relations
    Australian Category Seminar, February 2025.
    [Abstract, Slides]
  • Categorical Hilbert Theory
    QuaCS Seminar, February 2025.
    [Slides]
  • M*-categories
    Australian Category Seminar, January 2025.
    [Abstract, Slides]
  • Minimal dilations categorically
    ItaCa Fest and Edinburgh Category Theory Seminar, September 2024.
    [Handout, Video]
  • Abelian groups are to abelian categories as Hilbert spaces are to what?
    UCLouvain-ULB-VUB Category Theory Seminar, April 2024.
    [Handout]
  • Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
    (with Chris Heunen)
    Edinburgh Category Theory Seminar, February 2024;
    The Oxford Advanced Seminar on Informatic Structures, February 2024;
    Atlantic Category Theory Seminar, February 2024;
    Topology Seminar at UL Lafayette, April 2024;
    Junior Category Theory Seminar at UC Louvain, April 2024;
    Category Theory, June 2024;
    Foundational Methods in Computer Science, July 2024.
    [Handout]
  • Enriched Bisimulations
    (with Bryce Clarke)
    Proofs and Algorithms seminar, January 2024.
    [Handout]
  • Abstract Contractions
    (with Chris Heunen)
    Edinburgh Category Theory Seminar, October 2023.
    [Handout]
  • Bypassing Solèr’s Theorem: The Key to Axiomatising Dagger Categories of Finite-Dimensional Hilbert Spaces
    (with Chris Heunen)
    Applied Category Theory, August 2023.
    [Extended abstract, Video, Handout]
  • Enriched Bisimulations
    (with Bryce Clarke)
    Applied Category Theory, August 2023.
    [Extended abstract, Video, Handout]
  • Enriched Retrofunctors and Enriched Lenses
    (with Bryce Clarke)
    Symposium on Compositional Structures, April 2023.
    [Video, Handout]
  • Limits of Sequences via Colimits of Contractions
    (with Chris Heunen)
    Categorical Late Lunch, April 2023.
    [Handout]
  • Recognising retromorphisms retrospectively
    (with Bryce Clarke)
    Virtual Double Categories Workshop, November 2022.
    [Abstract, Video, Handout]
  • Enriched lenses
    (with Bryce Clarke)
    Applied Category Theory, July 2022.
    [Extended abstract, Video, Handout]
  • Universal indexed categories
    Topology, Algebra, and Categories in Logic, June 2022.
    [Abstract, Handout]
  • Universal indexed categories
    Categorical Late Lunch, March 2022.
    [Handout]
  • Proxy pullbacks in the category of lenses
    Australian Category Seminar, December 2021.
    [Abstract, Handout]
  • Polynomial functors and families parametrised by comonoids
    Category Theory 20→21, September 2021.
    [Abstract, Video, Handout]
  • The category of lenses is regular-ish
    Australian Category Seminar, August 2021.
    [Abstract, Handout]
  • Polynomials in Symmetric Monoidal Categories
    Australian Category Seminar, January 2021.
    [Abstract, Handout I, Handout II]
  • A Data Layout Description Language for Cogent
    (with Zilin Chen, Liam O’Connor, Partha Susarla, Christine Rizkallah and Gabriele Keller)
    Principles of Secure Compilation, January 2019.
    [Abstract, Handout]