- Cubical Type Theory Inside a Presheaf Topos (Summer '22) pdf
Summer '22 internship, for my Master's thesis. I worked on the use of Kripke-Joyal semantics to prove that the presheaves over the category of free de Morgan algebras are a model of cubical type theory. Here are the slides for my defense. I was supervised by Pierre-Louis Curien.
- Category theory in Coq (January '22) github
Final project of the LMFI's course 'Functional programming and formal proofs in Coq' where a student and I (re)implemented basics of category theory in Coq.
- Loops of Csörgő Type and the AIM Conjecture (Summer '21) pdf
Summer '21 internship. I worked on the AIM conjecture and tried to develop a computational approach to find Csörgő loops (a certain kind of non-associative structure) of size less than 128. Interestingly enough, the AIM conjecture was solved (independently of me!) by Michael Kinyon and Bob Veroff during my internship. Some of my code can be found here. You can find here the slides of a talk I gave during this internship, and here the slides for my defense.
- SYCO10 - Edinburgh (December '22) slides
Cubical type theory inside a presheaf topos.
- Adjunctions, monads, and monadicity (2022) pdf
This paper is a self-contained proof, in full details, and from (almost) scratch, of the monadicity theorem. We only assume the reader to be familiar with the basics of categories, functors, natural transformations, and the notion of coequalizer. We will give some examples and applications in further work.
- Category theory as a general tool for structures (2022) pdf
An internship report in which I argue that category theory serves as a syntactic tool for studying very general types of structures. I give some foundational justifications with Husserl's phenomenology, and I continue with the study of social interactions seen as Kan extensions. In French.
- On the Yoneda Lemma (2022) pdf
Small paper where I try to give some intuition about the notion of presheaf, prove the Yoneda Lemma and the density formula.