André Joyal | |
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Born |
Drummondville, Quebec, Canada | February 25, 1943
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]
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.
Joyal was born in Drummondville (formerly Saint-Majorique). He has three children and lives in Montreal.
André Joyal | |
---|---|
![]() | |
Born |
Drummondville, Quebec, Canada | February 25, 1943
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]
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.
Joyal was born in Drummondville (formerly Saint-Majorique). He has three children and lives in Montreal.