André Joyal
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
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