| ftp://triples.math.mcgill.ca/pub/rags/music/beatlabs.ps.gz, *19930423* TAPE I (1962-1964) Side A Besame Mucho (Velasquez/Skylar) 6 June 1962 This is the only surviving tape from the Beatles' E.M.I. audition for George Martin. Featuring Pete Best on drums, who was dismissed from the group a few months later. This song was almost released on the aborted |

| ftp://triples.math.mcgill.ca/pub/reyes/orkp.ps, *19931004* 10 Reference, Kinds and Predicates Marie La Palme Reyes, John Macnamara and Gonzalo E. Reyes The aim of this paper is to present a theory of reference for proper names (PNs), count nouns (CNs) and predicables (mainly adjectives, adjectival phrases, verbs, verb phrases). The paper is divided into three |

| ftp://triples.math.mcgill.ca/pub/seldin/elb.ps, *19931029* Note on -Reduction and Labelling Bound Variables in Typed >=-Calculus Garrel Pottinger Mathematical Sciences Institute 409 College Avenue Cornell University Ithaca, New York 14850, USA garrel@msiadmin.cit.cornell.edu Jonathan P. Seldiny Department of Mathematics Concordia University Montr eal, Qu ebec, |

| ftp://triples.math.mcgill.ca/pub/pavlovic/mapsI-US.ps.Z, *19931123* Maps I: relative to a factorisation system Du<=sko Pavlovi c |

| ftp://triples.math.mcgill.ca/pub/barr/acyclic.models.ps, *19940706* Acyclic models Michael Barr Department of Mathematics and Statistics McGill University Montreal, Quebec, Canada Email: barr@math.mcgill.ca 1994-07-06 |

| ftp://triples.math.mcgill.ca/pub/barr/CE.cohomology.ps, *19940710* Cartan-Eilenberg cohomology and triples Michael Barr 1994-02-01 |

| ftp://triples.math.mcgill.ca/pub/barr/topop.quasi-var.ps, *19940910* Topop is a quasi-variety Michael Barr and M. Cristina Pedicchio September 10, 1994 |

| ftp://triples.math.mcgill.ca/pub/rags/ccp/psss.ps.gz, *19941102* A Hyperdoctrinal View of Concurrent Constraint Programming Prakash Panangaden School of Computer Science McGill University Montr eal, Qu ebec, Canada Vijay Saraswat Xerox PARC Palo Alto, California, USA P.J. Scott University of Ottawa Ottawa, Ontario, Canada R.A.G. Seely McGill University and John |

| ftp://triples.math.mcgill.ca/pub/rags/ccp/psss-1.ps.gz, *19941103* A Hyperdoctrinal View of Constraint Systems Prakash Panangaden , McGill University Vijay Saraswat, Xerox PARC P. J. Scotty, University of Ottawa R. A. G. Seelyz, McGill University and John Abbott College |

| ftp://triples.math.mcgill.ca/pub/rags/music/continuo.ps.gz, *19941118* Basics of the basics of lute continuo Arto Wikla November 1994 The starting point for lute continuo learning 1. Learn to read bass staff fluently and to play it musically. Play whatsoever bass lines you happen to meet. (Already this ability makes you a useful partner for a |

| ftp://triples.math.mcgill.ca/pub/rags/nets/llsac.ps.gz, *19941122* LINEAR LOGIC, -AUTONOMOUS CATEGORIES AND COFREE COALGEBRAS1 R.A.G. Seely |

| ftp://triples.math.mcgill.ca/pub/rags/ptime/ptreal.ps.gz, *19941122* Graded Multicategories of Polynomial-time Realizers R.A.G. Seely Department of Mathematics and Computer Science John Abbott College, Ste. Anne de Bellevue and McGill University, Montr eal, Qu ebec Extended Abstract|Preliminary Version |

| ftp://triples.math.mcgill.ca/pub/rags/nets/polylin.ps.gz, *19941122* Polymorphic Linear Logic and Topos Models R.A.G. Seely |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun4.ps.gz, *19941128* 3. Anabicategories In a two-dimensional category, for a given pair of objects (0-cells), the totality of arrows (1-cells) from one to the other form a category; in short, arrows are objects in categories, and thus, one should attempt to determine them only up to isomorphism. This means that, for a given |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch9.ps.gz, *19941128* 7. The sketch specification of monoidal categories The difficulty in sketch-specifying the concept of monoidal category is with arranging that the morphisms of sketches become in the doctrine the not necessarily strict monoidal functors. To achieve this effect, we modify the concept of monoidal category |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch4.ps.gz, *19941128* 2. Sketch semantics Let S be an arbitrary category; we talk about "sketches" when referring to objects of S since in the applications S will be a sketch-category obtained by the constructions described in 1. Let r:R A @ R' be an arbitrary arrow in S . We say that a sketch S S satisfies r , in symbols S |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch2.ps.gz, *19941128* Introduction A completeness theorem asserts the equality of the formal deducibility relation and the semantic consequence relation in a particular logic. Algebraic Logic, and in particular, Categorical Logic replaces a completeness theorem by a representation theorem. Witness the examples of the Stone |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch5.ps.gz, *19941128* 3. Formal deductions of sketch entailments For motivation, we first consider the simple example of a possible way the category S presented by a c-sketch S may be constructed. S comes with a canonical "embedding" g :S A @ S ; note that we are identifying the category S with the corresponding sketch as in |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch3.ps.gz, *19941128* 1. Categories of sketches ffiffi Let G be a category, and K= K a (small) indexed set of objects K of G . We K Q K R define a new category G j K , the category of sketches over G with specification names the ffi elements of Q K R , and specification types the objects K of G for K Q K R . The objects of G |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun7.ps.gz, *19941128* References J. Benabou, Introduction to bicategories. In: Reports of the Midwest Category Seminar, Lecture Notes in Math. 47, Springer-Verlag, 1967; pp. 1-77. J. Benabou, Fibered categories and the foundations of naive category theory. J. Symbolic Logic 50(1985), 10-37. A. Blass, |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch8.ps.gz, *19941128* 6. Further examples In this section, we will see that the method of specifying a doctrine by sketches is not restricted to adjointness doctrines. I will first consider the concept of Grothendieck topology . I restrict attention (because of the interest in completeness; see the next section) to |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch10.ps.gz, *19941128* 8. Kinds of completeness For our purposes here, we will have to be specific about size-restrictions. In our previous definitions of categories, we restricted objects to be small; we had in mind (as usual) a certain fixed but arbitrary Grothendieck universe U , and "small" meaning "belonging to U |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch12.ps.gz, *19941128* References J. Adamek and J. Rosicky, Locally Presentable and Accessible Categories. London Mathematical Society Lecture Note Series 189, Cambridge University Press, 1994. H. Andreka and I. Nemeti, Injectivity in categories to represent all first order formulas, I. Demonstratio Math. 12(1979), |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun2.ps.gz, *19941128* Avoiding the axiom of choice in general category theory by M. Makkai (McGill University) Introduction In Category Theory, there is an underlying principle according to which the right notion of "equality" for objects in a category is isomorphism. Let me refer to the principle as the principle of |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch11.ps.gz, *19941128* 9. Sketch semantics versus Tarskian semantics In this section, I explain how Tarski-type semantics can be related to sketch-semantics. This may contribute to a better understanding of sketch-semantics. We will see that compactness in the usual sense for a generalized quantifier with a specific semantics |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun5.ps.gz, *19941128* 4. The anabicategory of saturated anafunctors The saturated composition of two saturated anafunctors (or sanafunctors, for short) is obtained by saturating the ordinary composite introduced in 1. Since saturation involves taking quotients of equivalence relations, it is natural to define the composite |

| ftp://triples.math.mcgill.ca/pub/makkai/gabbay.ps.gz, *19941128* On Gabbay s proof of the Craig interpolation theorem for intuitionistic predicate logic by Michael Makkai* (McGill University) |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun3.ps.gz, *19941128* 1. Anafunctors Let X and A be categories. An anafunctor F with domain X and codomain A , in a notation F:X A @ A , or just simply F:X A @ A , is given by the following data 1.(i),(ii) and conditions 1.(iii)-(v): 1.(i) A class Q F R , with maps s Q F RA @ Ob(X) ("source"), t Q F RA @ Ob(A) ("target"). Q |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch1.ps.gz, *19941128* Generalized sketches as a framework for completeness theorems by M. Makkai (McGill University) Contents: Introduction p. 1 1. Categories of sketches p. 8 2. Sketch semantics p. 21 3. Formal deductions of sketch-entailments p. 29 4. Specifying operations defined as adjoints p. 43 5. Exactness properties |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch6.ps.gz, *19941128* 4. Specifying operations defined as adjoints F. W. Lawvere s discovery that underlies categorical logic is that "all logical operations arise as adjoints", possibly in an iterative fashion. For the last qualification, think of the notion of exponentiation (in a Cartesian closed category) that arises as |

| ftp://triples.math.mcgill.ca/pub/makkai/sketch/sketch7.ps.gz, *19941128* 5. Exactness properties Exactness properties of structured categories abound in category theory; "coproducts are stable under pullback", "equivalence relations are effective" are examples. There are important ones involving infinitary operations (e.g., "filtered colimits of mono s is a mono"), but in |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun6.ps.gz, *19941128* 5. The effects of weak versions of the axiom of choice. In the previous parts of the paper, we left open whether the bicategory AnaCat is Cartesian closed. In this section, we show that a very weak version of the AC, one that is consistent with the negations of most of the usual special cases of the AC, |

| ftp://triples.math.mcgill.ca/pub/makkai/anafun/anafun1.ps.gz, *19941128* Avoiding the axiom of choice in general category theory by M. Makkai (McGill University) Contents: Introduction p. 1 1. Anafunctors p. 8 2. Adjoint anafunctors p. 37 3. Anabicategories p. 47 4. The anabicategory of saturated anafunctors p. 72 5. The effects of weak versions of the axiom of choice p. 79 |

| ftp://triples.math.mcgill.ca/pub/barr/algcomp.ps, *19950114* Algebraically compact functors Michael Barr Department of Mathematics and Statistics McGill University Montreal, Quebec, Canada H3P 1S4 Email: barr@triples.math.mcgill.ca 1995-01-14 |

| ftp://triples.math.mcgill.ca/pub/barr/fuzzy.models.ps, *19950122* Fuzzy models of linear logic Michael Barr Department of Mathematics and Statistics McGill University Montreal, Quebec, Canada Email: barr@math.mcgill.ca 1995-01-22 1 Introduction There has long been a perception among fuzzy set theorists that the negation based on the operation a 7! 1 a is the correct" |

| ftp://triples.math.mcgill.ca/pub/blute/lauchli.ps.Z, *19950320* Linear L auchli Semantics R. F. Blute P. J. Scott Dept. of Mathematics University of Ottawa Ottawa, Ontario CANADA March 20, 1995 Dedicated to the memory of Moez Alimohamed |

| ftp://triples.math.mcgill.ca/pub/pavlovic/CLCI.ps.gz, *19950322* Categorical logic of concurrency and interaction. I: Synchronous processes Du<=sko Pavlovi c |

| ftp://triples.math.mcgill.ca/pub/blute/hopf.ps.Z, *19950430* Hopf Algebras and Linear Logic Richard F. Blute University of Ottawa Ottawa, Ontario CANADA email address: rblute@acadvm1.uottawa.ca April 29, 1995 |

| ftp://triples.math.mcgill.ca/pub/rags/music/isoatd_1.ps.gz, *19950502* G 4 S G Bm Am D G Bm Am D G 4 VG Am !z Bm BB D G Bm Am D G 4 G Am !z Bm BB D Dm "b r (! ! BB E 4# |

| ftp://triples.math.mcgill.ca/pub/rags/music/isoatd_2.ps.gz, *19950502* In Spite of All the Danger Words by Ed Chen, Bruce Dumes and saki Music by .mau. G 4444 " = 120 1.2.3. A7 B7 I(I) (If I) V know know told E allither too would to - well hurt day, B that hershe'd and we she'd be |

| ftp://triples.math.mcgill.ca/pub/pavlovic/mapsII-US.ps.Z, *19950606* Maps II: Chasing diagrams in categorical proof theory Du<=sko Pavlovi c Dedicated to Jim Lambek in friendship and admiration |

| ftp://triples.math.mcgill.ca/pub/pavlovic/mapsII-A4.ps.Z, *19950606* Maps II: Chasing diagrams in categorical proof theory Du<=sko Pavlovi c Dedicated to Jim Lambek in friendship and admiration |

| ftp://triples.math.mcgill.ca/pub/rags/music/trobador.ps.gz, *19950607* The following paper was originally posted to rec.music.early. I have set it in PostScript for my use, changing only the oddities of ascii typesetting. The original newsgroup posting is available where you got this: ftp://triples.math.mcgill.ca/pub/rags/ragstriples.html |

| ftp://triples.math.mcgill.ca/pub/rags/music/lmt.ps, *19950612* Love Mee Tender Missing page of the Koenigsburg MS 1 a a a a a a aa a a a a a a a aa a 9 a |

| ftp://triples.math.mcgill.ca/pub/otto/thesis.ps.gz, *19950613* Complexity Doctrines James R. Otto, Jr. Department of Mathematics and Statistics McGill University, Montreal A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements of the degree of Doctor of Philosophy. June 13, 1995 c James R. Otto, Jr., 1995 ii |

| ftp://triples.math.mcgill.ca/pub/reyes/negation.ps, *19950825* Models for Non-Boolean Negations in Natural Languages Based on Aspect Analysis M. La Palme Reyes, J. Macnamara, G. E. Reyes and H. Zolfaghari May 1995 |

| ftp://triples.math.mcgill.ca/pub/rags/music/lirmb.ps.gz, *19950907* Side 1 1. Interview 2. 20 Flight Rock 3. I'll Keep You Satisfied 4. Step Inside Love 5. It's For You 6. Slow Down 7. This Boy 8. Hold Me Tight 9. If I Fell 10.The Night Before 11.Things We Said Today 12.Interview Side 2 1. I Feel Fine 2. Help! 3. Norwegian Wood 4. You've Got to Hide Your Love Away 5. |

| ftp://triples.math.mcgill.ca/pub/rags/ccp/mpss.ps.gz, *19951005* Nordic Journal of Computing 2(1995), 181{220 A LOGICAL VIEW OF CONCURRENT CONSTRAINT PROGRAMMING NAX P. MENDLER Department of Mathematics University of Ottawa Ottawa, Ontario, Canada nmendler@csi.uottawa.ca PRAKASH PANANGADENy School of Computer Science McGill University Montreal, Quebec, Canada |

| ftp://triples.math.mcgill.ca/pub/rags/oktoberfest.ps, *19951016* Oktoberfest Category Theory Meeting 14 { 15 October 1995 Montr eal, Canada Saturday morning 9:00{9:30 Peter Freyd Paracategories 9:35{10:10 Francisco Marmolejo Continuous families of models 10:15{10:45 Bob Rosebrugh Minimal Realization and Process Bicategories 11:05{11:35 Dan Christensen Phantom |

| ftp://triples.math.mcgill.ca/pub/rags/nets/nets.ps.gz, *19951028* Natural deduction and coherence for weakly distributive categories R.F. Blute1 J.R.B. Cockett2 R.A.G. Seely3 T.H. Trimble4 |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds3.ps.gz, *19951108* 3. Quantificational fibrations The notation and terminology of is used. The particular kinds of fibrations introduced here do not appear in loc.cit., but most of the needed ingredients do. E E C Let CP CP be a fibration; let Q be a class of arrows in B . Assume: B B C B has a terminal object, and |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldsd.ps.gz, *19951108* Appendix D: Calculations for 7. D1. Define the generalized DS vocabulary L as the full subcategory of L 2-cat anabicat on the objects of L , with relations I , I , T , H , T ; it is generalized since a 2-cat 1 2 1 2 non-maximal object, T , is also made into a relation. Accordingly, an L -structure is a |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds1.ps.gz, *19951108* 1. Logic with dependent sorts First, we describe the kinds of structure which the assertions of logic with dependent sorts are about. It is well-known from categorical logic that the similarity types that are graphs (having sorts the objects, and unary sorted operation symbols only) are sufficient for |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds2.ps.gz, *19951108* 2. Formal systems In this section, a vocabulary L for logic with dependent sorts is assumed fixed. Relations, formulas, etc., are all from/over L . For a formula j , Var ( j ) is "the set of all variables in j , free or bound". More precisely, Var ( j ) = Var( j ) for atomic j ; Var ( jUy ) = Var ( j |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds7.ps.gz, *19951108* 7. Equivalence of bicategories For 2-categories and bicategories, see , , . In this section, I discuss invariance of properties of bicategories, and of diagrams in bicategories, under biequivalence (however, I will call "biequivalence" "equivalence of bicategories"). To mention just two |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldsa.ps.gz, *19951108* Appendix A: An alternative introduction of logic with dependent sorts. The way we defined the basic concepts of FOLDS in 1 may look somewhat ad hoc because of the a priori role of the one-way (simple) categories as vocabularies. There is a more direct definition of FOLDS which does not start with |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds4.ps.gz, *19951108* 4. The syntax of first order logic with dependent sorts as a fibration Let L be a DSV; let K be the full subcategory of the kinds. Consider the category B=BK which is the free finite-limit completion of K : i:K A@ B , and for any category S with finite limits, i :Lex(B,S) A @ Fun(K,S) is an equivalence |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldsint.ps.gz, *19951108* First Order Logic with Dependent Sorts, with Applications to Category Theory by M. Makkai McGill University Preliminary version (Nov 6, 1995) Contents: Introduction p. 1 1. Logic with dependent sorts p. 14 2. Formal systems p. 32 3. Quantificational fibrations p. 39 4. The syntax of first-order logic |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldsc.ps.gz, *19951108* Appendix C: More on L equivalence and equality. Ordinary multisorted first-order logic without equality and without operation symbols (only relations are allowed) is a special case of FOLDS as follows. Let L be a multisorted, purely relational vocabulary. We associate a DSV L with L . The kinds of L are |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldsref.ps.gz, *19951108* References J. C. Baez and J. Dolan, Higher dimensional algebra and topological quantum field theory. Preprint (University of California, Riverside). J. Barwise, Back and forth through infinitary logic. In: Studies in Model Theory, ed. M. Morley, MAA Studies in Mathematics, vol. 8, The |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldsb.ps.gz, *19951108* Appendix B: A fibrational theory of L equivalence E E CD Consider fibrations CP DP , and the category Fib of all maps B B CD M2 E A @ E CD M=(M , M ) : CA@D CPD (1) 1 2 B A @ B C M D 1 of fibrations; Fib is a full subcategory of |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds6b.ps.gz, *19951108* Let T = (L , S ) be the theory of I-diagrams of categories, diag diag diag functors, and natural transformations. T is a theory in ordinary multisorted logic diag with equality. The models of T are those L -structures that are diag diag isomorphic to some D:I A@ Cat as an L |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/foldse.ps.gz, *19951108* Appendix E: More on equivalence and interpolation In this section, S and T are small Heyting categories, L is a DSV , K its category of kinds, and F:L A@ S , G:L A@ T are S- , resp. T-valued L-structures. Mod(S) denotes the S category of coherent functors S A@ Set , a full subcategory of Set ; similarly |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds5.ps.gz, *19951108* 5. Equivalence Let L be a fixed DSV, K the full subcategory of its kinds. We have defined what an L-structure is; even, what a C-valued L-structure is, for any C with finite limits. In what follows, we will make the minimal assumption that C is a regular category (which is equivalent to saying that P |

| ftp://triples.math.mcgill.ca/pub/makkai/folds/folds6a.ps.gz, *19951108* 6. Equivalence of categories, and of diagrams of categories The simplest application of the results of the last section is to invariance under equivalence of categories of first order properties of diagrams of objects and arrows in a category. In what follows, until further notice, L stands for L , the |

| ftp://triples.math.mcgill.ca/pub/barr/ctcs.elec.supp.ps, *19951113* CATEGORY THEORY FOR COMPUTING SCIENCE The electronic supplement Michael Barr Charles Wells Copyright c 1995 by Michael Barr and Charles Frederick Wells Contents Preface iii 1 Finite discrete sketches 1 1.1 Sketches with sums 1 1.2 The sketch for fields 3 1.3 Term algebras for FD sketches 5 2 More about |

| ftp://triples.math.mcgill.ca/pub/barr/termobj.ps, *19960119* Terminal coalgebras for endofunctors on sets Michael Barr Department of Mathematics and Statistics McGill University Montreal, Quebec, Canada H3P 1S4 Email: barr@triples.math.mcgill.ca 1993-05-07 |

| ftp://triples.math.mcgill.ca/pub/barr/asymm.ps, *19960205* Non-symmetric -autonomous categories Michael Barr Department of Mathematics and Statistics McGill University Montreal, Quebec, Canada Email: barr@math.mcgill.ca 1995-09-20 1 Introduction In (hereafter known as SCAT) the theory of -autonomous categories is outlined. Basically such a category |

| ftp://triples.math.mcgill.ca/pub/barr/newasymm.ps, *19960415* The Chu construction Michael Barr 1996-04-15 |

| ftp://triples.math.mcgill.ca/pub/cubric/frccc.ps.gz, *19960531* Embedding of a Free Cartesian Closed Category into the Category of Sets Djordje <=Cubri c |

| ftp://triples.math.mcgill.ca/pub/pavlovic/CCPS1.ps.gz, *19960622* Convenient Category of Processes and Simulations I: Modulo Strong Bisimilarity Du<=sko Pavlovi c |

| ftp://triples.math.mcgill.ca/pub/pavlovic/CCPS2.ps.gz, *19960622* Convenient categories of processes and simulations II: asynchronous cases Du<=sko Pavlovi c |

| ftp://triples.math.mcgill.ca/pub/pavlovic/chuI.ps.gz, *19960622* Math. Struct. in Comp. Science (1993), vol. 11, pp. 1{000 Copyright c Cambridge University Press Chu I: cofree equivalences, dualities and -autonomous categories Du<=sko Pavlovi cy Department of Computing, Imperial College, London SW7 2BZ, UK Received We study three comonads derived from the comma |

| ftp://triples.math.mcgill.ca/pub/pavlovic/CLNA.ps.gz, *19960622* Categorical logic of names and abstraction in action calculi D. Pavlovi c COGS, University of Sussex, Brighton, UK e-mail: duskop@cogs.susx.ac.uk |

| ftp://triples.math.mcgill.ca/pub/barr/ctcs.ansbook.ps, *19960724* ANSWERS TO ALL THE PROBLEMS in CATEGORY THEORY FOR COMPUTING SCIENCE" (Second Edition) Michael Barr and Charles Wells July 23, 1996 i Michael Barr Department of Mathematics and Statistics McGill University 805 Sherbrooke St. W. Montr eal, Qu ebec Canada H3P 1S4 barr@triples.math.mcgill.ca Home Page: |

| ftp://triples.math.mcgill.ca/pub/rags/wk_dist_cat/wdc.ps.gz, *19960726* Weakly distributive categories J.R.B. Cockett R.A.G. Seelyy |

| ftp://triples.math.mcgill.ca/pub/rags/bang/context0.ps.gz, *19960902* Categories for computation in context and unified logic: the intuitionist" case R.F. Blute1 J.R.B. Cockett2 R.A.G. Seely3 Presented to Peter Freyd to mark the occasion of his 60th birthday |

| ftp://triples.math.mcgill.ca/pub/cubric/interpol.ps.gz, *19960919* Interpolation Property for Bicartesian Closed Categories Djordje <=Cubri c March 14, 1994 |

| ftp://triples.math.mcgill.ca/pub/blute/shufA4.ps.gz, *19960923* The Shuffle Hopf Algebra and Noncommutative Full Completeness R. F. Blute P. J. Scott Dept. of Mathematics University of Ottawa Ottawa, Ontario K1N 6N5 CANADA August 30, 1996 |

| ftp://triples.math.mcgill.ca/pub/blute/shuf.ps.gz, *19960923* The Shuffle Hopf Algebra and Noncommutative Full Completeness R. F. Blute P. J. Scott Dept. of Mathematics University of Ottawa Ottawa, Ontario K1N 6N5 CANADA August 30, 1996 |

| ftp://triples.math.mcgill.ca/pub/otto/wp6.ps.gz, *19960929* Resolution cospans, axiom elimination, and fibrations J. Otto September 27, 1996 Introduction We outline a bicategorical approach to logic programming using the examples of addition and of fibrations with 1 locally small over 1. The second example, although degenerate, is related both to tiered |

| ftp://triples.math.mcgill.ca/pub/rags/bang/bang.ps.gz, *19961004* Math. Struct. in Comp. Science (1996), vol. 6, pp. 313{351 Copyright c Cambridge University Press ! and Storage as tensorial strength R. F. BLUTE,1y J. R.B. COCKETT,2z and R.A.G. SEELY3x 1 Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, ON, K1N6N5, Canada. |

| ftp://triples.math.mcgill.ca/pub/rags/bang/context1.ps.gz, *19961015* Categories for computation in context and unified logic R.F. Blute1 J.R.B. Cockett2 R.A.G. Seely3 Presented to Peter Freyd to mark the occasion of his 60th birthday |

| ftp://triples.math.mcgill.ca/pub/cubric/ccc_yn.ps.gz, *19961023* Normalization and the Yoneda Embedding Djordje <=Cubri c Peter Dybjery Philip Scottz October 13, 1996 |

| ftp://triples.math.mcgill.ca/pub/cubric/universal.ps.gz, *19970109* On the Semantics of the Universal Quantifier Djordje <=Cubri c |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multappe.ps, *19971003* Appendix We prove the if direction of 3.(1). We use the notation introduced in and before the statement of 3.(1). On the basis of the data L , C , F defined on L , and q , satisfying the f f L conditions in the definition of the free multicategory, we have to define F:C A@ D , including q f f A We write |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multsec7.ps, *19971003* 7. The category of multitopes ffiffiffiffiffi Suppose S=(C , C , D , d ) , S=(C , C , D , d ) are multitopic sets. A n n n n n n n n n n ffiffi morphism F :S A@ S of multitopic sets consists of maps F :C A@ C such that n n n F and F combine to induce a, necessarily unique, strict morphism of n n+1 ffi |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/mults1p2.ps, *19971003* T( b )=T( a (p)) . (5) The intuitive idea behind the operation W , called function-replacement, is that aWb is the p function obtained by evaluating, at the place p and only at that place, the function-variable a (p) as the composite function b . The condition (5) says that b is of the same type as a |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multsec5.ps, *19971003* 5. A 2 level multicategory with non standard amalgamation Let L be a language, and C a (not necessarily standard, but 1-level) multicategory free over L (see section 4). For a A=A(C) , we define a to be "the tuple of occurrences of operation symbols in a , listed from the left to the right". For a |

| ftp://triples.math.mcgill.ca/pub/rags/music/bc.ps.gz, *19971003* 1. It Won't Be Long 2. Tell Me Why 3. Misery A 4. Hello Little Girl 5. I'll Be Back 6. Flying 7. The Honeymoon Song 8. Love of the Loved 9. Love You To 10. Baby You're a Rick Man 11. Every Body's Got Something To Hide : : : 12. Please Please Me 13. If I Needed Someone 14. Rain 15. Yesterday 16. All My |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multintr.ps, *19971003* Introduction In and , John C. Baez and James Dolan have introduced a concept of weak higher dimensional category. The present paper is inspired by the work of Baez and Dolan. It is the first of two papers in which a modification of the Baez/Dolan proposal is offered and described in detail. |

| ftp://triples.math.mcgill.ca/pub/rags/billfest.ps, *19971003* Friday, September 26 8:45{ 9:30 Andr e Joyal The theory of h-categories 9:40{10:10 Marta Bunge Functions vs Distributions on Grothendieck toposes 10:20{10:50 Jonathon Funk Complete Spreads in Topos Theory 2:30{ 3:15 Pierre Cartier Computation and visualization: a new philosophy of categories 3:25{ 3:55 |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/mults234.ps, *19971003* 2. Multicategories For =, 2, ..., } ; , and h( j ) for . O is the set of all tuples of elements of O . O is the |

| ftp://triples.math.mcgill.ca/pub/rags/nets/fill.ps.gz, *19971003* Theory and Applications of Categories, Vol. 3, No. 5, 1997, pp. 85{131. PROOF THEORY FOR FULL INTUITIONISTIC LINEAR LOGIC, BILINEAR LOGIC, AND MIX CATEGORIES J.R.B. COCKETT AND R.A.G. SEELY Transmitted by Michael Barr |

| ftp://triples.math.mcgill.ca/pub/boshuck/david.ps, *19971003* DEFINABILITY AND DESCENT DAVID BALLARD AND WILLIAM BOSHUCK Introduction The present note offers a short argument for the descent theorems of Zawadowski (1995, originally 1989) and Makkai (1993), which were conjectured by Pitts after the descent theorem of Joyal & Tierney (1984) for open geometric |

| ftp://triples.math.mcgill.ca/pub/rags/BarrTalks.ps, *19971003* Barrfest Schedule May 29-31, 1997 THURSDAY 9:00{ 9:55 Murray Gerstenhaber Developments from Barr's thesis 10:00{10:25 George Janelidze On Barr's results on Galois theory in topoi, and further developments from topoi to general categories 11:00{11:55 Fred E J Linton HomB(B;B) and all that 12:00{12:25 |

| ftp://triples.math.mcgill.ca/pub/cubric/yonnorm.ps.gz, *19971003* To appear in: Math. Struct. in Comp. Science (199 ), vol. , pp. Copyright c Cambridge University Press Normalization and the Yoneda Embedding DJORDJE <= CUBR I C 1 y , PETER DYBJER 2 z and PH I L I P SCOTT 3 x 1 DPMMS, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, UK. e-mail: |

| ftp://triples.math.mcgill.ca/pub/blute/abp.ps, *19971003* Nuclear and Trace Ideals in Tensored -Categories Samson Abramsky Department of Computer Science University of Edinburgh Edinburgh, Scotland Richard Blutey Department of Mathematics and Statistics University of Ottawa Ottawa, Ontario, Canada Prakash Panangadenz BRICS Department of Computer Science Aarhus |

| ftp://triples.math.mcgill.ca/pub/rags/linear/linmorph.ps.gz, *19971003* Linearly distributive functors J.R.B. Cockett a;1 R.A.G. Seely b;2 a Department of Computer Science, University of Calgary, 2500 University Drive, Calgary, AL, T2N 1N4, Canada. b Department of Mathematics, McGill University, 805 Sherbrooke St., Montr eal, QC, H3A 2K6, Canada. Presented to Michael Barr |

| ftp://triples.math.mcgill.ca/pub/rags/linear/wdc.ps.gz, *19971003* Weakly distributive categories J.R.B. Cockett R.A.G. Seelyy This is the corrected" version of the published paper Journal of Pure and Applied Algebra 114 (1997) 133{ 173. The comments added in proof" in that paper are incorporated into the body of the text in this version. |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multrefs.ps, *19971003* References J. Baez and J. Dolan, Higher-dimensional algebra and topological quantum field theory, Journal of Mathematical Physics 36 (1995), 6073-6105. J. Baez and J. Dolan, letter to R. Street, Nov. 30, 1995, corrected version as of Dec. 3, 1995; available at |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/mults1p1.ps, *19971003* 1. An informal description 1.1. n graphs and multitopic sets. In the classical, strict, concept of higher-dimensional category (HDC), an HDC A consists of k-cells in each of several dimensions k , where k ranges over a set {0, ..., n} ( n-category), or over all natural numbers ( w -category). Let us |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multtitl.ps, *19971003* On weak higher dimensional categories by Claudio Hermida!," and Michael Makkai#,$ Department of Mathematics and Statistics McGill University% and John Power&,' Department of Computer Science University of Edinburgh( |

| ftp://triples.math.mcgill.ca/pub/makkai/multitopicsets/multsec6.ps, *19971003* 6. Multitopic sets An multitopic set S , by definition, consists of data (i) to (iii), subject to conditions (iv) to (viii): (i) a sequence C of sets , k k (ii) sequences C D of |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/phnll.ps, *19971029* Phase semantics for mixed non-commutative classical linear logic Paul Ruet LIENS-CNRS, Ecole Normale Sup erieure 45 rue d'Ulm, 75005 Paris, France Phone: +33 1 44 32 20 83 Fax: +33 1 44 32 20 80 Email: ruet@dmi.ens.fr April 1997 |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/csl97.ps, *19971029* Concurrent Constraint Programming and Mixed Non-Commutative Linear Logic Paul Ruet, Fran cois Fages LIENS-CNRS, Ecole Normale Sup erieure 45 rue d'Ulm, 75005 Paris, France Phone: +33 1 44 32 20 83 Fax: +33 1 44 32 20 80 Email: fruet,fagesg@dmi.ens.fr |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/ccnll97.ps, *19971029* Concurrent Constraint Programming and Non-Commutative Logic Paul Ruet, Fran cois Fages LIENS-CNRS, Ecole Normale Sup erieure 45 rue d'Ulm, 75005 Paris, France Phone: +33 1 44 32 20 83, Fax: +33 1 44 32 20 80 Email: fruet,fagesg@dmi.ens.fr |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/these-eng.ps, *19971029* PhD Thesis Universit e Denis Diderot, Paris 7 Non-commutative logic and constraint concurrent programming Paul Ruet |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/these.ps, *19971029* Th ese de Doctorat de l'Universit e Denis Diderot, Paris 7 Logique et Fondements de l'Informatique Logique non-commutative et Programmation concurrente par contraintes Paul Ruet Directeur de th ese: Fran cois Fages Rapporteurs: Yves Lafont Vijay Saraswat Soutenue le 23 octobre 1997 Jury: Michele Abrusci |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/CP96.ps, *19971029* Logical semantics of concurrent constraint programming Paul Ruet1;2 1 LIENS, Ecole Normale Sup erieure, 45 rue d'Ulm, 75005 Paris, France 2 Thomson - LCR, Domaine de Corbeville, 91404 Orsay, France Email: ruet@dmi.ens.fr |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/belnap.ps, *19971029* Complete sets of connectives and complete sequent calculus for Belnap's Logic Paul Ruet LIENS, Ecole Normale Sup erieure 45 rue d'Ulm, 75005 Paris, France Thomson - Laboratoire Central de Recherches Domaine de Corbeville, 91404 Orsay Cedex, France Email: ruet@dmi.ens.fr |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/gdr96.ps, *19971029* Programmes concurrents par contraintes et logique lin eaire non-commutative Paul Ruet, Fran cois Fages fruet,fagesg@dmi.ens.fr LIENS CNRS, Ecole Normale Sup erieure, Paris, France R esum e: Ce papier pr esente une connection pr ecise entre une version non-commutative de la logique lin eaire |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/TCS96.ps, *19971029* Combining explicit negation and negation by failure via Belnap's logic Paul Ruet, Fran cois Fages 1 Thomson - LCR, Domaine de Corbeville, 91404 Orsay, France, LIENS, Ecole Normale Sup erieure, 45 rue d'Ulm, 75005 Paris, France |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/nll1.ps, *19971029* Non-commutative linear logic with mobilities Paul Ruet LIENS, Ecole Normale Sup erieure, 45 rue d'Ulm, 75005 Paris, France Email: ruet@dmi.ens.fr |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/nll4.ps, *19971029* Non-commutative linear logic with mobilities Paul Ruet LIENS, Ecole Normale Sup erieure, 45 rue d'Ulm, 75005 Paris, France Email: ruet@dmi.ens.fr |

| ftp://triples.math.mcgill.ca/pub/ruet/PAPIERS/ccnll96.ps, *19971029* Concurrent Constraint Programming and Non-Commutative Linear Logic (Extended Abstract) Paul Ruet, Fran cois Fages fruet,fagesg@dmi.ens.fr LIENS-CNRS, Ecole Normale Sup erieure, Paris, France |

| ftp://triples.math.mcgill.ca/pub/ruet/THESE/exem.ps, *19971123* 1 Store ask tell c c { A ... B1 ... Bn ... |

| ftp://triples.math.mcgill.ca/pub/ruet/exem.ps, *19971123* 1 Store ask tell c c { A ... B1 ... Bn ... |

| ftp://triples.math.mcgill.ca/pub/ruet/lib/tex/elsartdoc.ps.gz, *19971123* PREPARING ARTICLES WITH LATEX INSTRUCTIONS TO AUTHORS FOR PREPARING COMPUSCRIPTS ELSEVIER SCIENCE PUBLISHERS B.V. PREPARING ARTICLES WITH LATEX INSTRUCTIONS TO AUTHORS FOR PREPARING COMPUSCRIPTS ELSEVIER SCIENCE PUBLISHERS B.V. This publication was typeset using LATEX TEX is a trademark of the American |

| ftp://triples.math.mcgill.ca/pub/ruet/plan.ps, *19971123* Th ese de Doctorat de l'Universit e Denis Diderot, Paris 7 Logique et Fondements de l'Informatique Logique non-commutative et Programmation concurrente par contraintes Paul Ruet Directeur de th ese: Fran cois Fages Rapporteurs: Yves Lafont Vijay Saraswat Soutenue le 23 octobre 1997 Jury: Michele Abrusci |

| ftp://triples.math.mcgill.ca/pub/ruet/elsartdoc.ps.gz, *19971123* PREPARING ARTICLES WITH LATEX INSTRUCTIONS TO AUTHORS FOR PREPARING COMPUSCRIPTS ELSEVIER SCIENCE PUBLISHERS B.V. PREPARING ARTICLES WITH LATEX INSTRUCTIONS TO AUTHORS FOR PREPARING COMPUSCRIPTS ELSEVIER SCIENCE PUBLISHERS B.V. This publication was typeset using LATEX TEX is a trademark of the American |

| ftp://triples.math.mcgill.ca/pub/ruet/THESE/plan.ps, *19971123* Th ese de Doctorat de l'Universit e Denis Diderot, Paris 7 Logique et Fondements de l'Informatique Logique non-commutative et Programmation concurrente par contraintes Paul Ruet Directeur de th ese: Fran cois Fages Rapporteurs: Yves Lafont Vijay Saraswat Soutenue le 23 octobre 1997 Jury: Michele Abrusci |

| ftp://triples.math.mcgill.ca/pub/blute/nuclear.ps.gz, *19980223* Nuclear and Trace Ideals in Tensored -Categories Samson Abramsky Department of Computer Science University of Edinburgh Edinburgh, Scotland Richard Blutey Department of Mathematics and Statistics University of Ottawa Ottawa, Ontario, Canada Prakash Panangadenz Department of Computer Science McGill |

| ftp://triples.math.mcgill.ca/pub/rags/linear/trace.ps.gz, *19980228* Feedback for linearly distributive categories: traces and fixpoints R.F. Blute a;1 J.R.B. Cockett b;2 R.A.G. Seely c;3 a Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, ON, K1N 6N5, Canada. b Department of Computer Science, University of Calgary, 2500 University Drive, |