André Joyal

André Joyal
Born	(1943-02-25) February 25, 1943 (age 78) Drummondville, Quebec, Canada
Nationality	Canadian
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 whose weak equivalences generalize both equivalence of categories and 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[]

• André Joyal, Myles Tierney, An extension of the Galois theory of Grothendieck, Memoirs of the American Mathematical Society 51 (1984), no. 309. doi:10.1090/memo/0309 MR0756176
• André Joyal, Quasi-categories and Kan complexes, (in Special volume celebrating the 70th birthday of Prof. Max Kelly) J. Pure Appl. Algebra 175 (2002), no. 1-3, 207—222 doi:10.1016/S0022-4049(02)00135-4.
• André Joyal, Myles Tierney, Quasi-categories vs Segal spaces, Categories in algebra, geometry and mathematical physics, 277—326, Contemp. Math. 431, Amer. Math. Soc., Providence, RI, 2007. arXiv:math.AT/0607820.
• André Joyal, Myles Tierney, On the theory of path groupoids, J. Pure Appl. Algebra 149 (2000), no. 1, 69—100, doi:10.1016/S0022-4049(98)00164-9.
• André Joyal, Ross Street, Pullbacks equivalent to pseudopullbacks, Cahiers topologie et géométrie différentielle catégoriques 34 (1993) 153-156; numdam MR1223657.
• André Joyal, Myles Tierney, Strong stacks and classifying space, Category theory (Como, 1990), 213—236, Lecture Notes in Math. 1488, Springer 1991.
• André Joyal, Ross Street, An introduction to Tannaka duality and quantum groups, Category theory (Como, 1990), 413—492, Lecture Notes in Math. 1488, Springer 1991 pdf.
• André Joyal, Ross Street, The geometry of tensor calculus I, Adv. Math. 88 (1991), no. 1, 55—112, doi:10.1016/0001-8708(91)90003-P; Tortile Yang-Baxter operators in tensor categories, J. Pure Appl. Algebra 71 (1991), no. 1, 43—51, doi:10.1016/0022-4049(91)90039-5; Braided tensor categories, Adv. Math. 102 (1993), no. 1, 20—78, doi:10.1006/aima.1993.1055.
• André Joyal, Ross Street, Dominic Verity, Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119 (1996), no. 3, 447—468.
• 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[]

• Interview with André Joyal (in French)
• André Joyal in nLab
• Official Web page at UQAM
• André Joyal at the Mathematics Genealogy Project