André Joyal

André Joyal (* 1943 in Drummondville ) is a Canadian mathematician, with category theory and topos theory and applications in algebra, logic, combinatorics, topology ( homotopy theory ) is concerned.

He is a professor at the Université du Québec à Montréal ( UQAM ).

He turned the category theory, among others, in the semantics of ( Kripke - Joyal semantics, by Saul Kripke ) and on combinatorial games by John Horton Conway and Combinatorics ( treatment generatrix functions in the Combinatorial Species theory).

He developed over several decades, the theory of the introduced in 1973 by JM Boardman and Rainer Vogt quasi- categories ..

In the late 1970s he developed a generalization of the Galois theory of Alexander Grothendieck with Miles Tierney, published in 1984 in the Memoirs of the American Mathematical Society.

With Ross Street he studied in the 1980s and 1990s with categories with tensor products, braid groups ( Braid ) and quantum group structures, motivated by applications in mathematical physics.

In the 1980s he developed a homotopy ( the type of model categories of Daniel Quillen ) on simplicial sets ( Joyal model structure or model structure on quasi- categories)

He is a Fellow of the Royal Society of Canada.

Writings

• With Miles Tierney on extension of the Galois theory of Grothendieck, American Mathematical Society 1984
• With Ieke Moerdijk Algebraic set theory, London Mathematical Society Lecture Note Series 220, Cambridge University Press 1995