André Joyal (French: [ʒwajal]; born 1943) is a professor of mathematics at the Université du Québec à Montréal who works on category theory.

He was a member of the School of Mathematics at the Institute for Advanced Study in 2013,[1] where he was invited to join the Special Year on Univalent Foundations of Mathematics.

[2] He discovered Kripke–Joyal semantics,[3] the theory of combinatorial species and with Myles Tierney a generalization of the Galois theory of Alexander Grothendieck[4] in the setup of locales.

He did some work on quasi-categories, after their invention by Michael Boardman and Rainer Vogt, in particular conjecturing[5] and proving the existence of a Quillen model structure on the category of simplicial sets whose weak equivalences generalize both equivalence of categories and Kan equivalence of spaces.

He co-authored the book "Algebraic Set Theory" with Ieke Moerdijk and recently started a web-based expositional project Joyal's CatLab [6] on categorical mathematics.