André Joyal

André Joyal (born 1943) is a professor of mathematics at the Université du Québec à Montréal who works on category theory. Joyal was born in Drummondville (formerly Saint-Majorique). He has three children and lives in Montreal. He was a member of the School of Mathematics at the Institute for Advanced Study in 2013. where he was invited to join the Special Year on Univalent Foundations of Mathematics.

He discovered Kripke–Joyal semantics, the theory of combinatorial species and with M. Tierney a generalization of the Galois theory of Grothendieck in the setup of locales. Most of his research is in some way related to category theory, higher category theory and their applications. He did the first real work on quasi-categories, after their invention by Boardman and Vogt, in particular conjecturing and proving the existence of a Quillen model structure on sSet 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 CatLabon categorical mathematics.