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 Québe ...

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, cate ...

. 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 scholar ...

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

Research

He discovered

Kripke–Joyal semantics Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Jo ...

, the theory of

combinatorial species In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures, which allows one to not merely count these structures but give bijective proofs invol ...

and with

Myles Tierney Myles Tierney (September 1937 – 5 October 2017) was an American mathematician and Professor at Rutgers University who founded the theory of elementary toposes with William Lawvere. Tierney obtained his B.A. from Brown University in 1959 and his ...

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 In mathematics, higher category theory is the part of category theory at a ''higher order'', which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher cate ...

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 In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called ' weak equivalences', ' fibrations' and 'cofibrations' satisfying certain axioms relating them. These abstr ...

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 Uni ...

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 List of the largest municipalities in Canada by population, second-most populous city in Canada and List of towns in Quebec, most populous city in the Provinces and territories of Canada, Canadian ...

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