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Canadian mathematician
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 .
Bibliography
Joyal, André;
Tierney, Myles (1984).
"An extension of the Galois theory of Grothendieck" .
Memoirs of the American Mathematical Society . 51 (309).
doi :
10.1090/memo/0309 .
MR
0756176 .
Joyal, A. (2002). "Quasi-categories and Kan complexes, (in Special volume celebrating the 70th birthday of Prof. Max Kelly)".
Journal of Pure and Applied Algebra . 175 (1–3): 207–222.
doi :
10.1016/S0022-4049(02)00135-4 .
Joyal, André; Tierney, Myles (2007). "Quasi-categories vs Segal spaces". Categories in Algebra, Geometry and Mathematical Physics . Contemporary Mathematics. Vol. 431. pp. 277–326.
arXiv :
math/0607820 .
doi :
10.1090/conm/431/08278 .
ISBN
9780821839706 .
MR
2342834 .
S2CID
119749421 .
Joyal, André; Tierney, Myles (2000). "On the theory of path groupoids".
Journal of Pure and Applied Algebra . 149 : 69–100.
doi :
10.1016/S0022-4049(98)00164-9 .
Joyal, André;
Street, Ross (1993).
"Pullbacks equivalent to pseudopullbacks" (PDF) . Cahiers de Topologie et Géométrie Différentielle Catégoriques . 34 (2): 153–156.
MR
1223657 .
Joyal, André; Tierney, Myles (1991). "Strong stacks and classifying spaces". Category Theory . Lecture Notes in Mathematics. Vol. 1488. pp. 213–236.
doi :
10.1007/BFb0084222 .
ISBN
978-3-540-54706-8 .
Joyal, André; Street, Ross (1991).
"An introduction to Tannaka duality and quantum groups" (PDF) . Category Theory . Lecture Notes in Mathematics. Vol. 1488. pp. 413–492.
doi :
10.1007/BFb0084235 .
ISBN
978-3-540-54706-8 .
Joyal, André; Street, Ross (1991). "The geometry of tensor calculus, I".
Advances in Mathematics . 88 : 55–112.
doi :
10.1016/0001-8708(91)90003-P . ; Joyal, A.; Street, R. (1993).
"Braided Tensor Categories" .
Advances in Mathematics . 102 : 20–78.
doi :
10.1006/aima.1993.1055 . ; Joyal, André; Street, Ross (1991).
"Tortile Yang-Baxter operators in tensor categories" .
Journal of Pure and Applied Algebra . 71 : 43–51.
doi :
10.1016/0022-4049(91)90039-5 .
Joyal, André; Street, Ross; Verity, Dominic (1996). "Traced monoidal categories".
Mathematical Proceedings of the Cambridge Philosophical Society . 119 (3): 447–468.
doi :
10.1017/S0305004100074338 .
S2CID
50511333 .
André Joyal,
Ieke Moerdijk , Algebraic set theory. London Mathematical Society Lecture Note Series 220. Cambridge Univ. Press 1995. viii+123 pp.
ISBN
0-521-55830-1
André Joyal, Myles Tierney, Notes on simplicial homotopy theory, CRM Barcelona, Jan 2008
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
arXiv :
math.CT/0305049 , 10.2).
References
External links
International National Academics People Other