Saturday, October 9 ---------------------------------------------------------------------------- Chair: J. Lambek 9:00 - 9:45 Andre Joyal, How to complete a category by freely adjoining all limits and colimits 9:50 - 10:20 Martin Markl, Deformations of everything 10:20 - 10:50 Break Chair: A. Joyal 10:50 - 11:20 Wim Ruitenburg, Yet another constructive logic 11:25 - 11:55 L Gaunce Lewis Jr, Equivariant Freudenthal suspension theorem 12:00 - 12:30 Robin Cockett, Copy Categories 12:30 - 2:00 Lunch Chair: R. Wood 2:00 - 2:30 Richard Wood, Distributive adjoint strings 2:35 - 3:05 Phil Scott (and M. Okada), Coherence and Undecidability for CCC's 3:10 - 3:40 Rick Blute, (Robert Seely and Robin Cockett) Contextual Logic 3:40 - 4:10 Break Chair: R. Rosebrugh 4:10 - 4:40 Andreas Blass, TBA 4:45 - 5:15 Bob Gordon (and John Power), Enrichment Through Variation 5:20 - 5:50 Jon Beck, TBA 6:30 - Reception Sunday, October 10 --------------------------------------------------------------------------- Chair: T. Fox 9:00 - 9:45 Till Plewe, When a locale product of metrizable spaces is spatial 9:50 - 10:20 Jonathan Smith (and A. Romanowska), Duality for semilattice representations 10:20 - 10:50 Break Chair: P. Scott 10:50 - 11:20 Peter Freyd, Hardware design and free allegories 11:25 - 11:55 Stacy Finkelstein, Tau Categories and Logic Programming 12:00 - 12:30 Kimmo Rosenthall, TBA 12:30 - 1:00 Break Chair: R. A. G. Seely 1:00 - 1:30 Jonathon Funk, The display locale of a cosheaf 1:35 - 2:05 Djordje Cubric, Interpolation property for bicartesian closed categories 2:10 - 2:40 Jim Otto, Categories and complexity Jon Beck TBA Andreas Blass <ablass@math.lsa.umich.edu> TBA Rick Blute <RBLUTE@acadvm1.uottawa.ca> Contextual Logic (joint with Robert Seely and Robin Cockett) Robin Cockett <robin@cpsc.ucalgary.ca> Copy Categories These are symmetric monoidal categories in which every object has a natural coassociative cocommutative comultiplication -- but no (natural) counit. Examples include the category of partial maps of a finitely complete category, the Kleisli category of the exception monad of a distributive category, ... I shall describe the category of "formal propositions" of a copy category and why this gives insight into the embedding of a distributive category into an extensive category (its the 2-category theory behind it!) Djordje Cubric <cubric@triples.math.mcgill.ca> Interpolation property for bicartesian closed categories Stacy Finkelstein <stacy@saul.cis.upenn.edu> Tau Categories and Logic Programming Peter Freyd <pjf@saul.cis.upenn.edu> Hardware design and free allegories Jonathon Funk <jfunk@morgan.ucs.mun.ca> The display locale of a cosheaf Bob Gordon <gordon@euclid.math.temple.edu> Enrichment Through Variation (joint with John Power) Andre Joyal <joyal@mipsmath.math.uqam.ca> How to complete a category by freely adjoining all limits and colimits L Gaunce Lewis Jr <gaunce@ichthus.syr.edu> Equivariant Freudenthal suspension theorem One of those nice situations when just a little touch of category theory cleans up a mess in topology. Martin Markl <> Deformations of everything Jim Otto <otto@triples.math.mcgill.ca> Categories and complexity Till Plewe <> When a locale product of metrizable spaces is spatial Kimmo Rosenthall <ROSENTHK@gar.union.edu> TBA Wim Ruitenburg <wimr@mscs.mu.edu> Yet another constructive logic Phil Scott <SCPSG@acadvm1.uottawa.ca> Coherence and Undecidability for CCC's (joint with M. Okada) We show the equational theory of simply typed lambda calculus with strong natural numbers object is undecidable, thus the coherence problem for equality of arrows in the free ccc with NNO is undecidable. We study the rewriting theory (made equational by Lambek's use of Mal'cev operators) and prove in fact the appropriate lambda calculus is not Church-Rosser, but is Strongly Normalizing. The latter proofs require heavy rewriting techniques. Jonathan Smith <jdhsmith@pollux.math.iastate.edu> Duality for semilattice representations (with A. Romanowska) We present general machinery for extending a duality between complete, cocomplete concrete categories to a duality between corresponding categories of semilattice representations. This enables known dualities to be regularised. Among the applications, regularised Lindenbaum-Tarski duality shows that the weak extension of Boolean logic (i.e. the semantics of PASCAL-like programming languages) is the logic for semilattice-ordered systems of sets. Another application enlarges Pontryagin duality by regularising it to obtain duality for commutative inverse Clifford monoids. Richard Wood <rjwood@cs.dal.ca> Distributive adjoint strings ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++