About Me
I am a second year PhD student at the University of Manchester studying category theory and its relation to logic, supervised by Nicola Gambino.
My current work has been on creating an algebraic model structure on categories internal to a Grothendieck topos inspired by “the effective model structure on simplicial objects” by Gambino, Henry, Sattler and Szumiło. The underlying model structure of this recovers the folk model structure of Everaert, Kieboom and Van Der Linden in their paper “Model Structures for Homotopy of Internal Categories”. By combining this with work from Gambino and Larrea on “Models of Martin-Löf type theory from algebraic weak factorisation systems” and results from Niefield and Pronk on “Internal Groupoids and Exponentiality” we are able to show that the $(\mathbf{TrivCof, Fib})$ algebraic weak factorisation system in the category $\mathbf{Gpd}(\mathcal{E})$ models Martin-Löf type theory. Importantly, this provides a constructive groupoidal model of MLTT with universes.
Relatedly, I am also collaborating with Adrian Miranda on The Elementary Theory of the 2-Category of Small Categories, which extends the elementary theory of the category of sets to a 2-dimensional setting.
I completed an MMath in Mathematics at the university of Sheffield in 2022. My MMath project was on the Dold-Kan correspondence, supervised by Prof. Sarah Whitehouse.