Joyal's CatLab North American School of Category Theory

Contents

Introduction

The North American School of Category Theory has emerged by the direct influence of Samuel Eilenberg and Saunders MacLane. My list of north american category theorists is certainly incomplete. There is also the question of deciding who is a category theorist and who is not. Many logicians and computer scientists have contributed to category theory. Many homotopy theorists have also contributed, for examples, Daniel Kan with adjoint functors and Peter May with operads. Quillen model structures, Stasheff polytopes and the localisation theory of Dwyer and Kan are now ubiquitous in higher category theory. There is a concentration of category theorists in Canada, mostly in Montreal, Halifax and Ottawa. There was also a small group of category theorists in Buffalo, but most are now retired or inactive.

One may question the idea that there is really a North American School of Category Theory. After all, category theory, and mathematics in general, ignores frontiers and continents. This maybe true in theory but it is false in practice. For example, the Grothendieck school has a definite european character, a continental character. One could also object to including people doing abstract homotopy theory like Daniel Kan and Bill Dwyer. It is true that there was few formal exchanges between category theorists and homotopy theorists during the last forty years. I recall meeting Bill Dwyer for the first time in 1985 at a meeting organised by Ronnie Brown in Bangor. Daniel Quillen was one of the speakers at the meeting to celebrate the 70th birthday of Eilenberg in 1984.

Categorical descendants of Eilenberg

• Alex Heller (Phd 1950)

  • Dana M. Latch (Phd 1971)

  • Noson S. Yanofsky (Phd 1996)

• David Buchsbaum (Phd 1954)

  • Peter Freyd (Phd 1960)

    • Murray Adelman (Phd 1960)

    • Marta Bunge (Phd 1966)

    • David Yetter (Phd 1984)

  • Barry Mitchel (Phd 1960)

    • Susan Niefield (Phd 1978)

• Daniel Kan (Phd 1955)

• William Lawvere (Phd 1963)

  • Marta Bunge (Phd 1966)

  • Anders Kock (Phd 1967)

    • Panagis Karazeris (Phd 1993)

  • Dietmar Schumacher (Phd 1969)

  • Michel Thiébaud (Phd 1972)

• Jonathan Beck (Phd 1964)

  • Pierre Malraison (Phd 1973)

• Harry Applegate (Phd 1965)

• Myles Tierney (Phd 1965)

  • Radu Diaconescu (Phd 1973)

  • Todd Trimble (Phd 1994)

  • Luca Mauri (Phd 1998)

Categorical descendants of Mac Lane

• John MacDonald (Phd 1965)

• Eduardo Dubuc (Phd 1969)

• Paul Palmquist (Phd 1969)

• Kathleen Edwards (Phd 1980)

• Steven Awodey (Phd 1997)

  • Michael Warren (Phd 2008)

The Buffalo group

• John Myhill (Phd 1949)

• John Duskin (Phd 1963)

  • John Glenn (Phd 1977)

  • Gary Nan Tie (Phd 1987)

• John Isbell (Phd 1954)

• William Lawvere (Phd 1963)

  • Kimmo Rosenthal (Phd 1979)

  • Emilio Faros Rivas (Phd 1991)

  • Michael Roy (Phd 1997)

• Stephen Schanuel (Phd 1963)

  • Yeong-Nan Yeh (Phd 1985)

The Halifax group

• Robert Paré (Phd 1969)

  • Richard Wood (Phd 1976)

    • William Garraway (Phd 2002)

    • Geoff Cruttwell (Phd 2008)

  • Robert Rosebrugh (Phd 1977)

  • Michael Wendt (Phd 1993)

  • Francisco Marmolejo (Phd 1995)

• Robert Dawson (Phd 1986)

• Dorette Pronk (Phd 1995)

• Peter Selinger (Phd 1997)

The Ottawa group

• Philip J. Scott (Phd 1976)

  • Esfandiar Haghverdi (Phd 2000)

• Richard Blute (Phd 1991)

• Peter Selinger (Phd 1997)

  • Benoît Valiron (Phd 2008)

  • Pieter Hofstra (Phd 2003)

The Montreal group

• Joachim Lambek (Phd 1950)

  • Dana Schlomiuk (Phd 1967)

    • Christiane Rousseau (Phd 1977)

  • Robert Paré (Phd 1969)

  • Robert Raphael (Phd 1969)

  • Joan Wick Pelletier (Phd 1970)

  • Fred Szabo (Phd 1971)

  • Colin Barry Jay (Phd 1984)

• Jean Maranda (Phd 1953)

  • Pierre Leroux (Phd 1970)

    • François Bergeron (Phd 1986)

• Michael Barr (Phd 1962)

  • Donavan Van Osdol (Phd 1969)

  • Thomas Fox (Phd 1977)

  • Po-Hsiang Chu (Phd 1982)

• Marta Bunge (Phd 1966)

  • Wendy Mac Caull (Phd 1984)

  • Murray Heggie (Phd 1986)

  • Felipe Gago Couso (Phd 1988)

  • Jonathon Funk (Phd 1992)

• Michael Makkai (Phd 1966)

  • Bill Boshuk

  • Hongde Hu (Phd 1992)

  • Alexandru Stanculescu (Phd 2008)

• Gonzalo Reyes (Phd 1967)

  • André Joyal

    • Luigi Santocanale (Phd 2000)

    • Alexandru Stanculescu (Phd 2008)

  • André Boileau (Phd 1975)

  • Giovanna Cifoletti (Phd 1988)

  • Marek Zawadowski (Phd 1989)

  • Houman Zolfaghari (Phd 1992)

  • Francois Magnan (Phd 1999)

• Robert Seely (Phd 1977)

Other category theorists in North America

• John Gray (Phd 1957)

  • Harvey Wolff (Phd 1970)

  • William Keigher (Phd 1973)

  • Larry Stout (Phd 1974)

  • Cameron Smith (Phd 1989)

• Fred Linton (Phd 1963)

  • Ernest Manes (Phd 1967)

  • George Reynolds (Phd 1973)

  • Hans Engenes (Phd 1976)

  • Osvaldo Acuna-Ortega (Phd 1977)

  • Zeev Barel (Phd 1981)

• Denis Higg (Phd 1970)

  • Philip J. Scott (Phd ?)

• Andreas Blass (Phd 1970)

  • Bagchi Atish (Phd 1991)

• Gaunce Lewis (Phd 1978)

• Andre Scedrov (Phd 1981)

  • Richard Blute (Phd 1991)

  • Peter Selinger (Phd 1997)

• John Baez (Phd 1986)

  • Laura Langford (Phd 1997)

  • Alissa Crans (Phd 2004)

  • Toby Bartels (Phd 2006)

  • Jeffrey Morton (Phd 2007)

• Marcelo Aguiar (Phd 1997)

• Thomas Fiore (Phd 2005)

• Claudio Hermida (Phd )

• Charles Wells (Phd )

• Mikhail Kapranov (Phd )

• Ezra Getzler (Phd 1986)

Computer scientists and logicians

• Dana Scott (Phd 1958)

  • Michael Fourman (Phd 1974)

  • Giuseppe Rosolini (Phd 1986)

  • Andrej Bauer (Phd 2000)

• Michael Makkai (Phd 1966)

• Gonzalo Reyes (Phd 1967)

• John Bell (Phd 1969)

• Andreas Blass (Phd 1971)

  • Bagchi Atish (Phd 1991)

• Vaughan Pratt (Phd 1972)

  • Vinet Gupta (Phd 1994)

• Andre Scedrov (Phd 1981)

  • Richard Blute (Phd 1991)

  • Peter Selinger (Phd 1997)

• Robin Cockett (Phd )

• Steven Awodey (Phd 1997)

  • Michael Warren (Phd 2008)

• Pieter Hofstra (Phd 2003)

Homotopy theorists

• Daniel Kan (Phd 1955)

  • Aldridge Bousfield (Phd 1966)

  • Stewart Priddy (Phd 1968)

  • Dror Farjoun (Phd 1971)

    • Boris Chorny (Phd 2003)

  • William Dwyer (Phd 1973)

    • Jan Spalinski (Phd 2000)

    • Bernard Badzioch (Phd 2000)

    • Julia Bergner (Phd 2005)

    • John Harper (Phd 2008)

  • Philip Hirschhorn (Phd 1977)

  • Jeffrey Smith (Phd 1981)

  • Stewart Priddy (Phd 1968)

• Jim Stasheff (Phd 1961)

  • Thomas Lada (Phd 1974)

• Peter May (Phd 1964)

  • Zbigniew Fiedorowicz (Phd 1975)

    • Cornel Balteanu (Phd 1997)

  • Anthony Elmendorf (Phd 1979)

  • Nicholas Kuhn (Phd 1980)

  • Michael Mandell (Phd 1997)

  • Daniel Isaksen (Phd 1999)

  • Benjamin Blander (Phd 2003)

  • Nick Gurski (Phd 2006)

  • Kate Ponto (Phd 2007)

  • Niles Johnson (Phd 2009)

  • Michael Schulman (Phd 2009)

• Daniel Quillen (Phd 1964)

  • Kenneth Brown (Phd 1971)

• Robert Thomason (Phd 1977)

• Students of Haynes Miller (Phd 1974):

  • Brooke Shipley (Phd 1995)

  • Daniel Christensen (Phd 1997)

  • Andrei Radulescu-Banu (Phd 1998)

  • Jesper Grodal (Phd 2000)

  • Hugh Robinson (Phd 2005)

  • Michael Ching (Phd 2005)

• Students of Mike Hopkins (Phd 1984):

  • Charles Rezk (Phd 1996)

  • Tibor Beke (Phd 1998)

  • Daniel Dugger (Phd 1999)

  • Sharon Hollander (Phd 2001)

  • Jacob Lurie (Phd 2004)

  • Andre Henriques (Phd 2005)

  • Samuel Isaacson (Phd 2009)

  • John Francis (Phd 2008)

Philosophers

• Colin McLarty (Phd )

• Jean-Pierre Marquis (Phd Philosophy 1988)

• Steven Awodey (Phd 1997)

  • Michael Warren (Phd 2008)