André Joyal (; born 1943) is a professor of mathematics at the
Université du Québec à Montréal
The (UQAM; ), is a French language, French-language public university, public research university based in Montreal, Quebec, Canada. It is the largest constituent element of the system.
UQAM was founded on April 9, 1969, by the government o ...
who works on
category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...
. He was a member of the School of Mathematics at the
Institute for Advanced Study
The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
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 (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...
of
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...
in the setup of locales. Most of his research is in some way related to
category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Category theory ...
,
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 morphism, arrows in order to be able to explicitly study the structure behind those equalities. H ...
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 the category of
simplicial set
In mathematics, a simplicial set is a sequence of sets with internal order structure ( abstract simplices) and maps between them. Simplicial sets are higher-dimensional generalizations of directed graphs.
Every simplicial set gives rise to a "n ...
s whose weak equivalences generalize both equivalence of categories and
Kan equivalence of spaces, which is now known as
Joyal model structure. 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
/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 ...
(formerly Saint-Majorique). He has three children and lives in Montreal
Montreal is the List of towns in Quebec, largest city in the Provinces and territories of Canada, province of Quebec, the List of the largest municipalities in Canada by population, second-largest in Canada, and the List of North American cit ...
.
Bibliography
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* André Joyal, Ieke Moerdijk, 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
See also
* Joyal's theorem
* Joyal's theta category
External links
Interview with André Joyal (in French)
*
Official Web page at UQAM
*
{{DEFAULTSORT:Joyal, Andre
Living people
1943 births
Category theorists
20th-century Canadian mathematicians
21st-century Canadian mathematicians
Academic staff of the Université du Québec à Montréal
People from Drummondville