# Nathanael Arkor

## narkor.co

## Postdoc researching Category Theory & Type Theory at Masaryk University

### Preprints

- Adjoint functor theorems for lax-idempotent pseudomonads (with Ivan Di Liberti and Fosco Loregian), , arXiv
- Relative monadicity (with Dylan McDermott), , arXiv
- The formal theory of relative monads (with Dylan McDermott), , arXiv
- Higher-order algebraic theories (with Dylan McDermott), , PDF

### Papers

- Abstract clones for abstract syntax (with Dylan McDermott), FSCD 2021, DOI, arXiv
- Algebraic models of simple type theories: a polynomial approach (with Marcelo Fiore), LICS 2020, DOI, arXiv

### Thesis

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

### Software

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

### Talks

- Relative monads and distributors (with Dylan McDermott), #LoVe Seminar, Slides
- The nature of adjoint functor theorems (with Ivan Di Liberti and Fosco Loregian), PSSL 108, Slides
- The formal theory of relative monads (with Dylan McDermott), Category Theory 2023, Slides
- The theory of relative (co)monads (with Dylan McDermott), Comonads Seminar, Slides
- The formal theory of relative monads (with Dylan McDermott), PSSL 107, Slides
- A 2-dimensional perspective on polymorphism, ICE-TCS Seminar, Slides
- Relative monads and their many guises (with Dylan McDermott), Octoberfest 2022, Slides
- What is a proof?, DIMEA and FORMELA Seminar, Slides
- The (relative) monad–theory correspondence (with Dylan McDermott), Masaryk University Algebra Seminar, Recording, Slides
- The (relative) monad–theory correspondence (with Dylan McDermott), TallCat, Slides
- The formal theory of theories (first half with Dylan McDermott), CT 20→21, Recording, Slides
- Abstract clones for abstract syntax (with Dylan McDermott), FSCD 2021, Recording, Slides
- Higher-order algebraic theories and relative monads (with Dylan McDermott), Categories and Companions Symposium 2021, Recording, Slides
- Higher-order algebraic theories and relative monads (with Dylan McDermott), Masaryk University Algebra Seminar, Recording, Slides
- Algebraic models of simple type theories: a polynomial approach (with Marcelo Fiore), LICS 2020, Recording, Slides
- Algebraic simple type theory: a polynomial approach (with Marcelo Fiore), Category Theory 2019, Slides