# André Joyal

André Joyal | |
---|---|

Born | Drummondville, Quebec, Canada | February 25, 1943

Known for | Quasi-categories Combinatorial species |

Scientific career | |

Fields | Category theory Homotopy theory |

Institutions | Université du Québec à Montréal |

**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]}

## Research

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. Most of his research is in some way related to category theory, higher category theory and their applications. 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.

## Personal life

Joyal was born in Drummondville (formerly Saint-Majorique). He has three children and lives in Montreal.

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