Joyal's CatLab
North American School of Category Theory



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

Categorical descendants of Mac Lane

The Buffalo group

The Halifax group

The Ottawa group

The Montreal group

Other category theorists in North America

Computer scientists and logicians

Homotopy theorists


Revised on May 9, 2013 at 23:02:52 by Tim Porter