In homotopy type theory, we construct the propositional truncation as a colimit, using only non-recursive higher inductive types (HITs). This is a first step towards reducing recursive HITs to non-recursive HITs. This construction gives a characterization of functions from the propositional truncation to an arbitrary type, extending the universal property of the propositional truncation. We have fully formalized all results in a new proof assistant, Lean.

I am currently a third year Ph.D. student in the Philosophy Department at Carnegie Mellon University. My advisor is Jeremy Avigad and I am also working together with Steve Awodey. I am enrolled in the Pure and Applied Logic program.

I previously studied at the Utrecht University in the Netherlands where I received a B.Sc. in Mathematics, a B.Sc. in Physics and a M.Sc. in Mathematics. My master thesis is Explicit convertibility proofs in Pure Type Systems supervised by Freek Wiedijk at the Radboud University Nijmegen. I was also trainer for the Dutch Mathematical Olympiad.