Seminars of the CENTRE de RECHERCHE en THEORIE des CATEGORIES CATEGORY THEORY RESEARCH CENTER C ---------> R | / | | / | | / | | / | v / v T ---------> C Tuesday, 12 Jan 1993 2:30 - 4:00 R. Blute (McGill U) "Linear topology and *-autonomous categories." Tuesday, 19 Jan 1993 2:30 - 4:00 R. Squire (McGill U) "Dualities for finite toposes" Tuesday, 26 Jan 1993 2:30 - 4:00 D. Pavlovic (McGill U) "Chasing proofs in the Lambek-Lawvere logic: On function comprehension" Tuesday, 2 Feb 1993 2:30 - 4:00 G. Reyes (U de Montreal) "Relative Boolean toposes and locales" (joint work with A. Kock) Tuesday, 9 Feb 1993 2:30 - 4:00 P. Panangaden (McGill U) "Old Foundations for linear logic: Holomorphic functions in Banach spaces as models of exponential types" Tuesday, 2 March 1993 2:30 - 4:00 M. Okada (Concordia U) "Mobile linear logic; pi calculus; chemical abstract machine" Tuesday, 16 March 1993 1:30 - 3:00 J. Baez "Categories, Tangles, and Quantum Gravity" Tuesday, 23 March 1993 3:30am - 5:00pm M. Okada (Concordia U) "Mobile linear logic; pi calculus; chemical abstract machine II" Tuesday, 30 March 1993 2:30am - 4:00pm M. Barr (McGill) "The diagram category of a category Tuesday, 13 April 1993 2:30pm - 4:00pm D. Cubric (McGill) "Interpolation property for Bicartesian Closed Categories" Tuesday, 20 April 1993 2:30pm - 4:00pm Arturo Sangalli (Champlain) "Endoprimal algebras and representation of clones" Tuesday, 27 April 1993 2:30pm - 4:00pm M. Makkai (McGill U) "General category theory without the axiom of choice." Tuesday, 4 May 1993 2:30pm - 4:00pm Silvia Ghilezan (McGill) "`Typed' proofs in untyped lambda calculus" Tuesday, 11 May 1993 2:30pm - 4:00pm P.J. Scott "Logical relations and computability predicates." Tuesday, 18 May 1993 2:30pm - 4:00pm P.J. Scott "On Milner's Pi-calculus and Linear Logic." Tuesday, 8 June 1993 2:30pm - 4:00pm S. Finkelstein (U Penn) "Tau-categories and logic programming" PLACE: BURNSIDE HALL 920, McGILL UNIVERSITY (COOKIES AND COFFEE AS USUAL AFTER THE TALK.) 1993 - 94 Tuesday 14 September 1993 2:30 - 4:00 pm M. Barr (McGill) *-autonomous categories revisited Tuesday 21 September 1993 2:30 - 4:00 pm Dj. Cubric McGill) "Interpolation for Bicartesian Closed Categories II" (No seminar 28 September) Tuesday 5 October 1993 2:30 - 4:00 pm N. Mendler (U Ottawa) Interaction Categories Tuesday 12 October 1993 2:30 - 4:00 pm L. Roman "On natural numbers in linear logic." Tuesday 19 October 1993 1:30 - 3:00 pm M. Markl "Cotangent cohomology, deformations of algebras and the coherence." 3:30 - 5:00 pm M. Gerstenhaber "Hecke algebras, $U_qsl(n)$ and the Donald-Flanigan conjecture for $S_n$" (Informal Abstract): The Donald-Flanigan conjecture says that if we take the group algebra of a finite group over a field of characteristic p dividing the order, so the group algebra can't be semisimple, then it is nevertheless possible to DEFORM the group algebra to a semisimple one. This seems to be one of the most intriguing problems in finite group theory. Previously, David J. Green in Essen and I had shown that this actually implies a purely group-theoretic consequence, which was subsequently proven by three group theorists in Essen, but they had to use the full classification theory of finite simple groups! Malka and I proved the conjecture for S_n. It has a little of the flavor of quantum groups in it. Tuesday 26 October 1993 2:30 - 4:00 pm J. Seldin (Concordia) "Eta-reduction and labelling bound variables" ABSTRACT: Note on $\eta$-Reduction and Labelling Bound Variables in Typed $\lambda$-Calculus by Garrel Pottinger and Jonathan P. Seldin It is well known that there are problems with the {\em labelled syntax} in type assignment to lambda-terms, the syntax in which the types of bound variables are indicated, as in $\la x : \sigma \bpb M$, since if $\eta$-reduction is added then the Church-Rosser Theorem fails in general (although it has been proved for some common systems of type assignment). In this paper, the labelled syntax is interpreted in the standard syntax by means of a constant \Label, so that $\la x : \sigma \bpb M$ is taken as an abbreviation for $\Label \sigma (\la x \bpb M)$. The constant \Label can be defined as a closed term, so that the labelled syntax is ultimately interpreted in a syntax for which the Church-Rosser Theorem is known to hold for both $\beta$-reduction and $\eta$-reduction. This interpretation is carried through for three well known systems of type assignment: ordinary type assignment, the second-order polymorphic typed lambda-calculus, and the calculus of constructions. These cases illustrate the general method for other systems of type assignment as well. Tuesday 2 November 1993 2:30 - 4:00 pm D. Pavlovic (McGill) "The Chu construction and cofree models of classical linear logic" Tuesday 9 November 1993 2:30 - 4:00 pm R. Squire (McGill) "Functional completeness of a Kuratowski-finite object of truth values in a topos" Tuesday 16 November 1993 2:30 - 4:00 pm J. Otto (McGill) "Linear time complexity and monoidal categories" Tuesday 23 November 1993 2:30 - 4:00 pm J. Otto (McGill) "Linear time complexity and monoidal categories II" Tuesday 30 November 1993 2:30 - 4:00 pm M. Makkai (McGill) "Higher dimensional categories" Tuesday 7 December 1993 2:30 - 4:00 pm Benoit Larose (MIT) "An application of the general Morita Theorem for algebraic theories" ABSTRACT: We discuss R. McKenzie's characterization of categorical equivalence between two varieties (equational classes) and present an application of this criterion to the study of completeness in multiple-valued logics. Let F be a closed set of operations on a finite set A for which we want to find a completeness criterion, i.e. determine the maximal closed subsets of F. Let G be a closed subset of F such that the variety V generated by the algebra is category equivalent to the variety W generated by some known algebra ; this equivalence induces a lattice isomorphism between the sets of closed sets containing G and G' which enables us to determine if G is maximal in F. We present several examples and certain extensions of this method.