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André Joyal

December 14, 2023

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]

André Joyal
Born (1943-02-25) February 25, 1943 (age 80)
Drummondville, Quebec, Canada
NationalityCanadian
Known forQuasi-categories
Combinatorial species
Scientific career
FieldsCategory theory
Homotopy theory
InstitutionsUniversité du Québec à Montréal

Research edit

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 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 and recently started a web-based expositional project Joyal's CatLab [6] on categorical mathematics.

Personal life edit

Joyal was born in Drummondville (formerly Saint-Majorique). He has three children and lives in Montreal.

Bibliography edit

  • 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
  • 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 edit

  1. ^ Institute for Advanced Study: A Community of Scholars
  2. ^ IAS school of mathematics: Univalent Foundations of Mathematics
  3. ^ Robert Goldblatt, A Kripke-Joyal semantics for noncommutative logic in quantales; Advances in Modal Logic 6, 209—225, Coll. Publ., London, 2006; MR2396933
  4. ^ 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.
  5. ^ A. Joyal, A letter to Grothendieck, April 1983 (contains a Quillen model structure on simplicial presheaves)
  6. ^ Joyal's CatLab

External links edit

December 14, 2023
andré, joyal, french, ʒwajal, born, 1943, professor, mathematics, université, québec, montréal, works, category, theory, member, school, mathematics, institute, advanced, study, 2013, where, invited, join, special, year, univalent, foundations, mathematics, bo. Andre Joyal French ʒwajal born 1943 is a professor of mathematics at the Universite du Quebec a Montreal 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 Andre JoyalBorn 1943 02 25 February 25 1943 age 80 Drummondville Quebec CanadaNationalityCanadianKnown forQuasi categoriesCombinatorial speciesScientific careerFieldsCategory theoryHomotopy theoryInstitutionsUniversite du Quebec a Montreal Contents 1 Research 2 Personal life 3 Bibliography 4 References 5 External linksResearch editHe 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 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 and recently started a web based expositional project Joyal s CatLab 6 on categorical mathematics Personal life editJoyal was born in Drummondville formerly Saint Majorique He has three children and lives in Montreal Bibliography editJoyal Andre 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 Andre 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 Andre 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 Andre Street Ross 1993 Pullbacks equivalent to pseudopullbacks PDF Cahiers de Topologie et Geometrie Differentielle Categoriques 34 2 153 156 MR 1223657 Joyal Andre 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 Andre 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 Andre 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 Andre 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 Andre 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 Andre 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 Andre Joyal Myles Tierney Notes on simplicial homotopy theory CRM Barcelona Jan 2008 pdf Andre 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 edit Institute for Advanced Study A Community of Scholars IAS school of mathematics Univalent Foundations of Mathematics Robert Goldblatt A Kripke Joyal semantics for noncommutative logic in quantales Advances in Modal Logic 6 209 225 Coll Publ London 2006 MR2396933 Joyal Andre Tierney Myles 1984 An extension of the Galois theory of Grothendieck Memoirs of the American Mathematical Society 51 309 doi 10 1090 MEMO 0309 A Joyal A letter to Grothendieck April 1983 contains a Quillen model structure on simplicial presheaves Joyal s CatLabExternal links editInterview with Andre Joyal in French Andre Joyal at the nLab Official Web page at UQAM Andre Joyal at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Andre Joyal amp oldid 1170977590, wikipedia, wiki, book, books, library,

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