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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.〔(Institute for Advanced Study: A Community of Scholars )〕 where he was invited to join the ''Special Year on Univalent Foundations of Mathematics''.〔(IAS school of mathematics: Univalent Foundations of Mathematics )〕
== Main research ==
He discovered Kripke–Joyal semantics,〔Robert Goldblatt, A Kripke-Joyal semantics for noncommutative logic in quantales; Advances in Modal Logic 6, 209--225, Coll. Publ., London, 2006; 〕 the theory of combinatorial species and with M. Tierney a generalization of the Galois theory of Grothendieck〔A. Joyal, M. Tierney, An extension of the Galois theory of Grothendieck, Mem. Amer. Math. Soc. 51 (1984), no. 309, vii+71 pp.〕 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〔A. Joyal, A letter to Grothendieck, April 1983 (contains a Quillen model structure on simplicial presheaves)〕 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 CatLab 〔(Joyal's CatLab )〕 on categorical mathematics.
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