André Joyal (; born 1943) is a professor of mathematics at the

Université du Québec à Montréal The Université du Québec à Montréal (English: University of Quebec in Montreal), also known as UQAM, is a French-language public university based in Montreal, Quebec, Canada. It is the largest constituent element of the Université du Qué ...

who works on

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, ca ...

. He was a member of the School of Mathematics at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

in 2013, where he was invited to join the ''Special Year on Univalent Foundations of Mathematics''.

Research

He discovered Kripke–Joyal semantics, the theory of combinatorial species and with Myles Tierney a generalization of the

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...

of Alexander Grothendieck in the setup of locales. Most of his research is in some way related to

, 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 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 Izak (Ieke) Moerdijk (; born 23 January 1958) is a Dutch mathematician, currently working at Utrecht University, who in 2012 won the Spinoza prize. Education and career Moerdijk studied mathematics, philosophy and general linguistics at the Un ...

and recently started a web-based expositional project Joyal's CatLab Joyal's CatLab
/ref> on categorical mathematics.

Personal life

Joyal was born in

Drummondville Drummondville is a city in the Centre-du-Québec region of Quebec, located east of Montreal on the Saint-François River. The population as of the Canada 2021 Census was 79,258. The mayor of Drummondville is Stéphanie Lacoste. Drummondville is ...

(formerly Saint-Majorique). He has three children and lives in

Montreal Montreal ( ; officially Montréal, ) is the second-most populous city in Canada and most populous city in the Canadian province of Quebec. Founded in 1642 as '' Ville-Marie'', or "City of Mary", it is named after Mount Royal, the triple- ...

Bibliography

* * * * * * * *; ; * * André Joyal,

, Algebraic set theory. London Mathematical Society Lecture Note Series 220. Cambridge Univ. Press 1995. viii+123 pp. * André Joyal, Myles Tierney, Notes on simplicial homotopy theory, CRM Barcelona, Jan 200
pdf
* André Joyal, Disks, duality and theta-categories, preprint (1997) (contains an original definition of a weak ''n''-category: for a short account see Leinster's , 10.2).

References

External links

*
Official Web page at UQAM
* {{DEFAULTSORT:Joyal, Andre Living people 1943 births Category theorists 20th-century Canadian mathematicians 21st-century Canadian mathematicians Université du Québec à Montréal faculty People from Drummondville