Seminars of the CENTRE de RECHERCHE en THEORIE des CATEGORIES CATEGORY THEORY RESEARCH CENTER C ---------> R | / | | / | | / | | / | v / v T ---------> C Tuesday, 27 January 1998 2:10 - 3:30 G Reyes (U Montreal) The law of motion in Special Relativity 4:00 - 5:00 M Barr (McGill) Cohomology: Introduction This is a topic in the "categorical aspects of physics seminar" (formerly the "operads seminar") Tuesday, 3 February 1998 2:00 - 3:30 J Lambek (McGill) Quaternions and the particles of physics 4:00 - 5:00 M Barr (McGill) Cohomology II "Categorical aspects of physics seminar" (formerly the "operads seminar") Tuesday, 10 February 1998 2:00 - 3:30 Alexy Davydov (Moscow, Concordia) Twisting of monoidal structures and representations of finite groups. 4:00 - 4:00 : N Yanofsky (McGill) Tensor categories, quantum groups and links Tuesday, 17 February 1998 2:00 - 3:30 : M Makkai (McGill) Multisorted Equational Algebraic Logic 4:00 - 5:00 : N Yanofsky (McGill) Tensor categories, quantum groups and links (II) Tuesday, 24 February 1998 Spring Break - no seminar Tuesday, 3 March 1998 2:00 - 3:30 : P Ruet and M Abrusci Commutativity and non-commutativity 4:00 - 5:00 : N Yanofsky (McGill) Tensor categories, quantum groups and links (III) Tuesday, 10 March 1998 2:00 - 3:30 : R. Blute (Ottawa) Nuclear and trace ideals in tensored *-categories 4:00 - 5:00 : P Panangaden (McGill) Conformal Field Theory a la Segal Tuesday, 17 March 1998 2:00 - 3:30 P Panangaden (McGill) Quinn's axioms and other matters Tuesday, 24 March 1998 2:00 - 3:30 PJ Scott (Ottawa) Geometry of Interaction and models of untyped combinatory logic 4:00 - 5:00 P Panangaden (McGill) Conformal Field Theory a la Segal Tuesday, 31 March 1998 2:00 - 3:30 E Haghverdi (Ottawa) Geometry of Interaction and models of untyped combinatory logic II Tuesday, 28 April 1998 1:30 - 3:00 P Panangaden (McGill) A profunctor model of dataflow networks Tuesday, 5 May 1998 2:00 - 3:30 : M Makkai (McGill) Some categorical logic, with applications to higher dimensional categories Tuesday, 12 May 1998 [ CANCELLED ] 2:00 - 3:30 : P Panangaden (McGill) A profunctor model of dataflow networks II Tuesday, 19 May 1998 2:00 - 3:30 : S Niefield (McGill, Union) Exponentiability and Fibrations Tuesday, 26 May 1998 2:00 - 3:00 : C Casadio Extended linguistic applications of non-commutative linear logic 3:30 - 4:30 : C Casadio Non-commutative linear logic and classical Lambek calculus: cut free proofs and logical constants Tuesday, 2 June 1998 2:00 - 3:30 : M Makkai (McGill) The essential finiteness of the definition of multitopic n-category ===================================== Tuesday, 1 Sept 1998 2:00 - 3:30 : R Cockett (Calgary) Restriction categories and categories of partial maps Tuesday, 8 Sept 1998 2:00 - 3:30 : J Koslowski (TU Braunschweig) Games and strategies via the Chu construction Tuesday, 15 Sept 1998 2:00 - 3:30 : M Makkai (McGill) Joyal's theta categories and their relations to protocategories Tuesday, 22 Sept 1998 2:00 - 3:30 : M. Fiore (Edinburgh) A semantic theory of higher-order syntax: An analysis of the differential equation X = V + X' + X^2 Tuesday, 29 Sept 1998 2:00 - 3:30 : E Landry (McGill - Philosophy Dept) Category Theory -- The Language of Mathematics 4:00 - 5:00 : S Crans (McGill) Introducing post-modern algebra according to Tuesday, 6 Oct 1998 2:00 - 3:30 : E Schlaepfer (McGill) On Chu-spaces and group algebras 4:00 - 5:00 : M. Barr (McGill) Simple duality for finite simplicial complexes An informal talk (POSTPONED: 2:00 - 3:30 : M. Bunge (McGill) Update on Discrete Giraud-Conduche Fibrations ) Tuesday, 13 Oct 1998 2:00 - 3:30 : Thomas Hildebrandt (BRICS Aarhus) A Realtional Model of Nondeterminate Dataflow Joint with P. Panangaden and G. Winskel Tuesday, 20 Oct 1998 2:00 - 3:30 : M Barr (McGill) On $*$-autonomous categories Tuesday, 27 Oct 1998 2:00 - 3:30 : J. Lamarche (UQAM - Linguistics) Semantic type in linguistic context ABSTRACT: In this presentation, I discuss the semantic content of the French verb ETRE 'to be' and its role in the definition of semantic types. The standard description of a copular verb like ETRE is that it relates a predicate argument () to an entity argument (). I argue that this description of ETRE is not appropriate because it encodes in the lexicon properties of syntactic constructions. This position follows from the minimal assumption that, in Generative Grammar, lexical description should be "terminal", that is, it should not include properties specific to the phrases and sentences where a lexical item occurs. Applying this terminality constraint, I argue that 1) ETRE selects one argument, and nothing else. The notion of entity arises when the verb is combined with its argument. 2) The categories that are relevant for the notion of entity are VP and PP--not NP as is generally assumed. 3) The ability of a phrase to be a predicate is not associated with a given part-of-speech category. Rather, predication arises through a specific mode of combination in syntax. I show that with a terminal description of ETRE, we can account for type-shifting phenomena that characterize the verb's different uses without resorting to type-shifting rules or multiple lexical representations. This approach makes us rethink our position on the role of syntax in accounting for type ambiguities, the mapping between conceptual, linguistic and logical categories, and the question of monosemy/homonymy/polysemy in the grammar of natural language. 4:00 - 5:00 : M Fiore (Sussex) A Theory of Recursive Domains with Applications to Concurrency ABSTRACT: I will present a 2-categorical theory for recursively defined domains generalising the traditional approach based on order-theoretic structures to category-theoretic ones. A motivation for this work is the need of a domain theory for concurrency with an account of bisimulation. This is joint work with Gian Luca Cattani and Glynn Winskel. An extended abstract with our results appeared in the Proceedings of LICS 1998. Tuesday, 10 Nov 1998 2:00 - 3:30 : S Crans (McGill) Braidings the post-modern way 4:00 - 5:00 : M Barr (McGill) Informal talk on *-autonomous categories Tuesday, 17 Nov 1998 2:00 - 3:30 : Masahiro Hamano (visiting U Ottawa) $Z$-modules and Full Completeness of Multiplicative Linear Logic Abstract: We prove that the full completeness theorem for MLL+Mix holds by the simple interpretation via formulas as objects and proofs as $Z$-invariant morphisms in the *-autonomous category of topologized vector spaces. We shall do this by generalizing the recent work of R. F. Blute and P. J. Scott (APAL '96) where they used the semantical framework of dinatural transformation introduced by Girard-Scedrov-Scott ('92). By omitting the use of dinatural transformation, our semantics evidently allows the interpretation of the cut-rule, while the original Blute-Scott's does not. Moreover, our interpretation for proofs is preserved automatically under the cut elimination procedure. (In this sense, our semantics is considered as a denotational semantics.) In our semantics proofs themselves are characterized by the concrete algebraic notion ``Z-invariance'', and our denotational semantics provides the full completeness. Our semantics is naturally extended to the full completeness semantics for $CyLL+Mix$ thanks to an elegant method of Blute-Scott (JSL `98) (which is their sequel of (APAL '96)). Tuesday, 24 Nov 1998 2:00 - 3:30 : Masahiro Hamano Pontrjagin Duality and a Full Completeness of Multiplicative Linear Logic Without the Mix Rule Abstract: While a semantical characterization of "provability" is expressed by the traditional notioin the followingn of "completeness", a semantical characterization of "proof" is expressed by the notion of "full-completeness". Various versions of full completeness theorem for MLL+Mix were proved by Abramsky-Jagadeesan(JSL'94), Loader(LICS'94), Blute-Scott(APAL'96), etc.. However, the Mix rule destroys the usual logical meaning of syntax since the distinction between truth and the falsehood collapses with the presence of the Mix rule. As for MLL without the Mix rule, a smaller number of full completeness theorems (Hyland-Ong's ('94) and A.Tan's ('97)) are known. In this talk, by using a mathematically more concrete framework than theirs, we prove the full completeness theorem for MLL WITHOUT the Mix rule. Our framework uses Barr's category of the topological abelian groups, and an MLL-proof is interpreted as a dinatural transformation of the category. We first prove the unique interpretation theorem for a binary provable sequent by a purely category-theoretical setting and method. Then we prove the completeness theorem for a binary sequent by investigating a mathematically concrete structure of the category, which is derived by the classical Pontrjagin duality theorem. Combining these theorems, we achieve to prove the full completeness theorem under the semantical framework ``associated binary space''. Tuesday, 1 Dec 1998 2:00 - 3:30 : C. Butz (McGill) Geometric morphisms and logic Abstract: The classifying topos theorem for geometric theories is certainly one of the highlights of the relationship between category theory and logic. Some of my recent research (partly together with Peter T. Johnstone and Steve Awodey) has centered around the question what can be said for other logics (like (full) first-order, first-order logic extended by quantification over functions, etc.). Though there do not exist classifying toposes (even when one restricts the class of geometric morphisms) there are good results available. The talk will survey some of them, including the sketch of topological completeness theorems for higher order logics. (References given on the web page.) COFFEE as usual after the talk PLACE: BURNSIDE HALL 920, McGILL UNIVERSITY =================================================== (Any comments, suggestions to rags@math.mcgill.ca)