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Category Theory at McGill

Silvia Bunge and Carl Christian Mikkelsen, Montreal '78


    1. Grothendieck's program was expounded by Grothendieck in his famous unpublished very long "Letter to Quilllen". In Montreal, Joyal, Makkai and Bunge are "pursuing the stacks" from different points of views.
    2. Lawvere's program was initiated by Lawvere in two steps, in 1967 and in 1983. The first is called "Categorical Dynamics" and it gave rise to "Synthetic Differential Geometry". In Montreal, both Reyes and Bunge have worked and formed many students in this area. The second is called "Distributions Theory on Toposes" and is still in full development.In Montreal, Bunge and her collaborators from elsewhere (A. Carboni (Como), J. Funk (Saskatchewan), S. Niefield (Union College), M. Fiore (Sussex), M. Jibladze (Louvain-la-Neuve and Tbilisi), and T. Streicher (Darmstadt) has been actively engaged in research in this area for the past seven years.
    3. Computational Category Theory. Broadly speaking, this includes Linear Logic, Chu Categories, Synthetic Domain Theory, Coherence, Bi-completions of Categories, Categorical Proof Theory, and Categorical Linguistics. In Montr\'eal, Lambek, Barr, Seely and others are actively working in some aspects of this program.


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