Prospects for Computer Formalization of Infinite-Dimensional Category Theory (Invited Talk)

Abstract

As mathematics becomes increasingly complicated, the prospect of using a computer proof assistant to (i) certify the correctness of one’s own work and (ii) interact with the formalized mathematical literature becomes increasingly attractive. In this talk, we will describe some challenges that arise when it comes to formalizing weak infinite-dimensional category theory, specifically the theory of ∞-categories developed by Joyal and Lurie. We introduce two parallel ongoing collaborative efforts to formalize ∞-category theory in two different proof assistants: Lean and Rzk. We show some sample formalized proofs to highlight the advantages and drawbacks of each formal system and explain how you could contribute to this effort. This involves joint work with Mario Carneiro, Dominic Verity, Nikolai Kudasov, and Jonathan Weinberger.