Nathanael Arkor

narkor.co

Postdoc researching Category Theory & Type Theory at Tallinn University of Technology

Google ScholarORCID

About me

Hi – I am a postdoctoral researcher in the Logic and Semantics Group at Tallinn University of Technology, working under Tarmo Uustalu. My present research interests fall broadly within pure category theory and type theory, and include more specifically: formal category theory, relative monads, double category theory, 2-category theory, abstract syntax & algebraic type theory, and categorical algebra & logic.

Previously, I was a postdoctoral researcher in the Algebra Group at Masaryk University, working under John Bourke. I completed my PhD in the Programming, Logic, and Semantics Group at the University of Cambridge with Marcelo Fiore.

I am happy to supervise bachelor's and master's projects in any of the areas mentioned above – feel free to email me to discuss potential projects.

Preprints

  1. Higher-order algebraic theories (with Dylan McDermott), , PDF
    See Chapter 4 of my thesis for an revised account.

Papers

  1. Relative monadicity (with Dylan McDermott), Journal of Algebra, , DOI, arXiv
  2. The nerve theorem for relative monads (with Dylan McDermott), Accepted for Theory and Applications of Categories, , arXiv
  3. Adjoint functor theorems for lax-idempotent pseudomonads (with Ivan Di Liberti and Fosco Loregian), Theory and Applications of Categories, , TAC, arXiv
  4. The formal theory of relative monads (with Dylan McDermott), Journal of Pure and Applied Algebra, , DOI, arXiv
  5. Abstract clones for abstract syntax (with Dylan McDermott), FSCD 2021, DOI, arXiv
  6. Algebraic models of simple type theories: a polynomial approach (with Marcelo Fiore), LICS 2020, DOI, arXiv

Thesis

  1. Monadic and Higher-Order Structure, University of Cambridge (2022), PDF, DOI

Software

  1. quiver: a modern commutative diagram editor for the web.
  2. tangle: a modern string diagram editor for the web.

Talks

  1. A recipe for enriched categories, TSEM Seminar, Slides
  2. The pullback theorem for relative monads (with Dylan McDermott), Category Theory 2024, Slides
  3. The pullback theorem for relative monads (with Dylan McDermott), TSEM Seminar, Recording, Slides
  4. Relative monads and distributors (with Dylan McDermott), #LoVe Seminar, Slides
  5. The nature of adjoint functor theorems (with Ivan Di Liberti and Fosco Loregian), PSSL 108, Slides
  6. The formal theory of relative monads (with Dylan McDermott), Category Theory 2023, Recording, Slides
  7. The theory of relative (co)monads (with Dylan McDermott), Comonads Seminar, Slides
  8. The formal theory of relative monads (with Dylan McDermott), PSSL 107, Slides
  9. A 2-dimensional perspective on polymorphism, ICE-TCS Seminar, Slides
  10. Relative monads and their many guises (with Dylan McDermott), Octoberfest 2022, Slides
  11. What is a proof?, DIMEA and FORMELA Seminar, Slides
  12. The (relative) monad–theory correspondence (with Dylan McDermott), Masaryk University Algebra Seminar, Recording, Slides
  13. The (relative) monad–theory correspondence (with Dylan McDermott), TallCat, Slides
  14. The formal theory of theories (first half with Dylan McDermott), CT 20→21, Recording, Slides
  15. Abstract clones for abstract syntax (with Dylan McDermott), FSCD 2021, Recording, Slides
  16. Higher-order algebraic theories and relative monads (with Dylan McDermott), Categories and Companions Symposium 2021, Recording, Slides
  17. Higher-order algebraic theories and relative monads (with Dylan McDermott), Masaryk University Algebra Seminar, Recording, Slides
  18. Algebraic models of simple type theories: a polynomial approach (with Marcelo Fiore), LICS 2020, Recording, Slides
  19. Algebraic simple type theory: a polynomial approach (with Marcelo Fiore), Category Theory 2019, Slides