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André Joyal

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André Joyal
Born (1943-02-25) February 25, 1943 (age 81)
Drummondville, Quebec, Canada
NationalityCanadian
Known forQuasi-categories
Combinatorial species
Scientific career
FieldsCategory theory
Homotopy theory
InstitutionsUniversité 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 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

References

  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