February 2017 - Categories - categories.org.au

ETAPS 2017 early registration deadline approaching
by Tarmo Uustalu 01 Mar '17

01 Mar '17

Early registration deadline 12 March 2017! ****************************************************************** CALL FOR PARTICIPATION 20th European Joint Conferences on Theory And Practice of Software ETAPS 2017 Uppsala, Sweden, 22-29 April 2017 http://www.etaps.org/2017 ****************************************************************** -- ABOUT ETAPS -- ETAPS is the primary European forum for academic and industrial researchers working on topics relating to software science. ETAPS, established in 1998, is a confederation of five main annual conferences, accompanied by satellite workshops. ETAPS 2017 is the twentieth event in the series. -- MAIN CONFERENCES (24-28 April) -- * ESOP: European Symposium on Programming (PC chair Hongseok Yang, University of Oxford, UK) * FASE: Fundamental Approaches to Software Engineering (PC chairs Marieke Huisman, Universiteit Twente, The Netherlands, and Julia Rubin, University of British Columbia, Canada) * FoSSaCS: Foundations of Software Science and Computation Structures (PC chairs Javier Esparza, Technische Universität München, Germany, Andrzej Murawski, University of Warwick, UK) * POST: Principles of Security and Trust (PC chairs Matteo Maffei, Universität des Saarlandes, Germany, Mark D. Ryan, University of Birmingham, UK) * TACAS: Tools and Algorithms for the Construction and Analysis of Systems (PC chairs Axel Legay, INRIA Rennes, France, and Tiziana Margaria, LERO, Ireland) TACAS '17 hosts the 6th Competition on Software Verification (SV-COMP). -- INVITED SPEAKERS -- * Unifying speakers: Michael Ernst (University of Washington, USA) Kim G. Larsen (Aalborg University, DK) * FoSSaCS invited speaker: Joel Ouaknine (University of Oxford, UK) * TACAS invited speaker: Dino Distefano (Facebook and Queen Mary University of London, UK) -- UNIFYING PUBLIC LECTURE Serge Abiteboul (DI, INRIA Paris & ENS Cachan, France) -- INVITED TUTORIALS Véronique Cortier (LORIA, CRNS, France) Kenneth McMillan (Microsoft Research Redmond, USA) -- CONTRIBUTED PAPERS, PROGRAMME -- See the accepted paper lists and conference programme at the conference website. -- SATELLITE EVENTS (22-23 April, 29 April) -- 16 satellite workshops and other events will take place before or after ETAPS 2017. DICE-FOPARA, GaLoP, GaM, SynCop-PV, VerifyThis (22-23 April) FESCA, SNR (22 April) HotSpot, QAPL, SannellaFest (23 April) BX, CREST, LiVe, MARS, PLACES, VPT (29 April) -- REGISTRATION -- Early registration is until Sunday, 12 March 2017 (23:59 GMT+1). http://www.etaps.org/2017/registration -- ACCOMMODATION -- The organizers have negotiated special rates from several hotels in Uppsala. To benefit from those, follow the instructions on the conference website. The offers expire on different dates. -- HOST CITY -- Uppsala city holds a rich history, having for long periods been the political, religious and academic centre of Sweden. Uppsala University is over 500 years old and ranked among the top 100 in the World and has hosted many great scientists over the years, for instance Carl von Linné, Anders Celsius and Anders Jonas Ångström. The proximity to the capital of Sweden, Stockholm, provides additional benefits as a potential site for arranging both pre- and post congress tours, as well as for excursions or tourism. -- HOST INSTITUTION -- ETAPS 2017 is hosted by the Department of Information Technology, Uppsala University. -- ORGANIZERS Parosh Abdulla (General chair), Mohamed Faouzi Atig, Andreina Francisco, Kaj Lampka, Philipp Rümmer, Konstantinos Sagonas, Björn Victor, Wang Yi, Tjark Weber, Yunyun Zhu [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

Bottom line to: Does equality between sets contradict the philosophy behind structural set theory?
by Leopold Schlicht 01 Mar '17

01 Mar '17

I'm thankful for all the both private and public emails I got in consequence of my question "Does equality between sets contradict the philosophy behind structural set theory?", especially the emails I got from Ingo Blechschmidt, Fred Linton, Bob Rosebrugh, and Marquis Jean-Pierre were helpful. Let me briefly sum up what I learnt: If one wants to be fussy, and looks to the question from a "formal system" point of view, then I'm right: Once one puts all morphisms in one big bag and talks about dom and codom as "functions" that both specify a *unique* objects, one can't get around using an equality between sets, which doesn't make sense in a setting of structural set theory. Instead, one should use the definition from *dependent type theory*: a category consists of a collection Ob of objects and for each pair (x, y) of objects in Ob a set Hom(x, y) of morphisms x -> y. Writing f: x -> y is then just a type declaration (and not a statement that is either true or false!) that declares f to be in the collection Hom(x, y). We are not supposed to compare morphisms of different type. But however, there should be a local equality on each set Hom(x, y) so that we can discuss when two morphisms f, g: x -> y of the same type are equal. But, as Fred Linton pointed out, natural language is quite flexible and being written in an informal language, as almost all math books are, one shouldn't interpret everything literally. Writing dom(f) = A for example should just abbreviate that we consider A to be the domain of f—the authors didn't intend to seriously discuss whether two sets are equal or not, it's just a piece of notation. Thus, there isn't really a fault in the book by Lawvere and Rosebrugh. Thanks again, Leopold [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

3 2

ETAPS 2018 call for satellite events
by Tarmo Uustalu 28 Feb '17

28 Feb '17

21st European Joint Conferences on Theory and Practice of Software ETAPS 2018 Thessaloniki, Greece, 14-21 April 2018 http://www.etaps.org/2018/ Call for Satellite Events -- ABOUT ETAPS -- The European Joint Conferences on Theory and Practice of Software (ETAPS) is the primary European forum for academic and industrial researchers working on topics relating to Software Science. It is an annual event held in Europe each spring since 1998. Its twenty-first edition, ETAPS 2018, will take place 14-21 April 2018 in Thessaloniki, Greece. ETAPS 2018 main conferences, scheduled for 16-20 April, are: * ESOP: European Symposium on Programming * FASE: Fundamental Approaches to Software Engineering * FOSSACS: Foundations of Software Science and Computation Structures * POST: Principles of Security and Trust * TACAS: Tools and Algorithms for the Construction and Analysis of Systems -- SATELLITE EVENTS -- The ETAPS 2018 organizing committee invites proposals for satellite events (workshops) that will complement the main conferences. They should fall within the scope of ETAPS. This encompasses all aspects of the system development process, including specification, design, implementation, analysis and improvement, as well as the languages, methodologies and tools which support these activities, covering a spectrum from practically-motivated theory to soundly-based practice. Satellite events provide an opportunity to discuss and report on emerging research approaches and practical experience relevant to theory and practice of software. ETAPS 2018 satellite events will be held immediately before and after the main conferences, on 14-15 April and 21 April. -- ARRANGEMENTS FOR SATELLITE EVENTS -- The organizers of an ETAPS 2018 satellite are expected to: * create and maintain a website for the event, * form a PC, produce a call for papers for the event (if appropriate), * advertise the event through specialist mailing lists etc. to complement the publicity of ETAPS, * review the submissions received and make acceptance decisions, * prepare an informal (pre)proceedings for the event (if appropriate), * prepare the event's program complying with any scheduling constraints defined by the ETAPS 2018 organizing committee, * prepare and organize the publication of a formal (post)proceedings (if desired). The ETAPS 2018 organizing committee will: * promote the event on the website and in the publicity material of ETAPS 2018, * integrate the event's program into the overall program of the conference, * arrange registration for the event as a component of registration for ETAPS, * collect a participation fee from the registrants, * produce a compilation USB memory stick of the informal (pre)proceedings of the satellite events of ETAPS 2018 and distribute this to the registrants, * provide the event with a meeting room of an appropriate size, A/V equipment, coffee breaks and possibly lunch(es). As a rule, ETAPS will not contribute toward the travel or accommodation costs of invited speakers or organizers of satellite events. -- SUBMISSION OF SATELLITE EVENT PROPOSALS -- Researchers and practitioners wishing to organize satellite events are invited to submit proposals to the workshop co-chairs Alexander Chatzigeorgiou <achat(a)uom.gr> and Nick Bassiliades <nbassili(a)csd.auth.gr> using the web form at http://eptcs.web.cse.unsw.edu.au/ETAPS/ . The following information is requested: * the name and acronym of the satellite event * the names and contact information of the organizers * the duration of the event: one or two days * the preferred period: 14 April, 15 April, 14-15 April or 21 April * the expected number of participants * a brief description (120 words approximately) of the event topic for the website and publicity material of ETAPS 2018 * a brief explanation of the event topic and its relevance to ETAPS * an explanation of the selection procedure of contributions to the event, the PC chair and members, if known already, information about past editions of the event, if applicable * any other relevant information, like a special event format, invited speakers, demo sessions, special space requirements, etc. * a tentative schedule for paper submission, notification of acceptance and final versions for the (informal pre-)proceedings (the ETAPS 2018 organizing committee will need the final files by the end of Feb. 2018) * the plans for formal publication (no formal publication, formal proceedings ready by the event, formal post-proceedings, publication venue - EPTCS or elsewhere) The proposals will be evaluated by the ETAPS 2018 organizing committee on the basis of their assessed benefit for prospective participants of ETAPS 2018. Prospective organizers may wish to consult the web pages of previous satellite events as examples: ETAPS 2017: http://www.etaps.org/2017/workshops ETAPS 2016: http://www.etaps.org/2016/workshops ETAPS 2015: http://www.etaps.org/2015/workshops ETAPS 2014: http://www.etaps.org/2014/workshops ETAPS 2013: http://www.etaps.org/2013/workshops ETAPS 2012: http://www.etaps.org/2012/workshops -- IMPORTANT DATES -- Satellite event proposals deadline: 24 March 2017 Notification of acceptance: 7 April 2017 -- HOST CITY -- Thessaloniki, named after Alexander's the Great sister, is the second largest city in Greece. Thessaloniki is an industrial and commercial center hosting an annual international trade fair, as well as a transportation hub with a major modern port and an international airport. Thessaloniki's history spans over 2300 years. Although largely rebuilt in modern style, Thessaloniki still retains its famous white Byzantine walls, the 15th century White Tower, and a Venetian citadel. The city is famous for its many fine Byzantine churches and Roman ruins of the triumphal arch and the palace of Emperor Galerius. Thessaloniki is a vibrant student city hosting more than 80,000 university students and offering countless options when it comes to local/international cuisine, cafes, music and day trips. ETAPS 2018 is organized by the Aristotle University of Thessaloniki, the largest university in Greece. -- FURTHER INFORMATION AND ENQUIRIES -- Please contact the workshop co-chairs, Alexander Chatzigeorgiou <achat(a)uom.gr> and Nikos Bassiliades <nbassili(a)csd.auth.gr>. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

Postdoc at Macquarie
by Richard Garner 28 Feb '17

28 Feb '17

Dear all, The category theory group at Macquarie is currently advertising a two-year Postdoctoral Research Fellowship to work on a project entitled "Enriched categories: new applications in geometry and logic". Applications close 31st March. The position is expected to start in the second half of this year. More information can be found at the following link: http://jobs.mq.edu.au/cw/en/job/500525/postdoctoral-research-fellow Feel free to contact me with further queries. Richard Garner [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

post-doc position announcement
by Dorette Pronk 27 Feb '17

27 Feb '17

If you have any questions about this position, don't hesitate to contact me. Dorette Pronk ------------------------------------- Post Doctoral Fellow Position Dalhousie University Nova Scotia Math Circles and the Department of Mathematics and Statistics Nova Scotia Math Circles and the Department of Mathematics and Statistics at Dalhousie University are advertising a post-doctoral fellowship with duties in outreach, outreach coordination, and communication. The post-doctoral fellow will spend 50% of their duties on research, and 50% on outreach and outreach coordination, see job description below. The academic supervisor of the PDF must be a member of the department of Mathematics and Statistics at Dalhousie University. Interested candidates should contact their proposed supervisor before the application. The outreach coordinator duties consist of the following: * Communicate with teachers and schoolboards * Organize outreach trips to schools in the province * Coordinate regular staff and casuals for school visits and outreach events * Maintain the Math Circles finances * Work with external relations and sponsors * Ensure continued funding for Math Circles as required The outreach coordinator should have received their PhD after July 2013 and before August 2017. They should have strong research skills, an interest in math outreach, good social and organizational skills, and experience in outreach as well as outreach and/or event coordination. Advantageous but not necessary are the following: experience with html and design programs, a driver???s license, and experience in fundraising with corporations. Terms of employment will conform to post-doctoral fellowship positions at Dalhousie University. The position is for one year, starting August 2017. The position is renewable for a second year subject to budgetary approval. For more information on Nova Scotia Math Circles, see http://www.nsmathcircles.com/ To apply, please send the following: * A cover letter, including the name of the proposed supervisor * A CV (which includes relevant experience on outreach and organization) * A teaching dossier with an emphasis on outreach * A brief research statement * A minimum of three reference letters: two on research and at least one, but preferably two, on outreach and administrative experience. This should be sent before March 15, 2017 via email to Queena Crooker-Smith at queena.smith(a)dal.ca [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

2 1

Does equality between sets contradict the philosophy behind structural set theory?
by Leopold Schlicht 26 Feb '17

26 Feb '17

Zermelo-Fraenkel set theory (with choice) is commonly accepted as the standard foundation of mathematics. It is a material set theory. This means that for every two objects/sets a,b one can ask whether a=b or not. Also, one can always ask whether "a is an element of b" is true or not. So "element" is a global element relation. As an alternative foundation for set theory, Lawvere proposed ETCS (= elementary theory of the category of sets). It is the standard example of a structural set theory. The idea behind structural set theory is that elements—in contrast to material set theory—have no internal structure, i.e. are just "abstract dots". Thus there there is no global element relation, and "objects" are not indepedent things, they always lie in a particular structure (for example, we cannot speak about 2 as an object that exists on its own, but we instead talk about the "2 in the structure IN" or the "2 in the structure IR", and strictly speaking, these are not the "same" objects, but we have a natural injection IN -> IR which maps the "natural number 2" to the "real number 2"). There have been controversial discussion whether ETCS is more appropriate as a foundation for mathematics than ZFC. I don't want to discuss this here, but want to point you to this paper: "Rethinking set theory" by Tom Leinster (it's available at the arxiv) in which Tom Leinster introduces ETCS and argues that this foundational system is much nearer to the practice of mathematicians than ZFC. Quite at the end of the paper, Leinster states that *Sets for Mathematics* by Lawvere and Rosebrugh is the quite the only book that teaches set theory in the flavour of structural set theory (ETCS)—which makes sense, since Lawvere is the "founder" of structural set theory. Now, let me come to my question: Does equality between sets contradict the philosophy behind structural set theory? Obviously, when doing set theory in the spirit of structural set theory, we *don't need equality between sets*. Instead, we talk about isomorphisms, which makes more sense structurally. Also, the typical definition of equality between sets (extensionality) can't be formulated in ETCS. Thus it seems to me that the notion of "equality between sets" doesn't make much sense in structural set theory. Of course, we could say that two sets are equal if there is a bijection between them, or state that equality exists between sets without further specifying what it does (in particular, if we identify all isomorphic sets, whether there are infinitely many isomorphic sets that are *not* equal, ...). But this wouldn't yield to additional value, and is thus superfluous. Having this thoughts in mind, I was surprised when I read the following in *Sets for Mathematics*—the standard text book for structural set theory (on page 2!): > Notation 1.1: The arrow notation f : A -> B just means the domain of f is A and the codomain of f is B, and we write dom(f) = A and cod(f) = B. Here, the authors talk about the equality of two sets (dom(f) = A). They also use the "big bag of morphisms"-definition of category and not the "by pairs (A, B) of objects indexed family of hom-sets". But in this definition, one must talk about operations dom and cod which specify for each morphism a unique domain and codomain. But the word "unique" here presupposes that we have a notion of equality between objects. Could someone from the categorical foundations of mathematics clarify my confusion? On the nLab (see nLab page on "category") there are two definitions of the term "category": "With one collection of morphisms" and "With a family of collections of morphisms", and to me it seems the second ("With a family of collections of morphisms") is more appropriate for structural set theory. But then, why do Lawvere—the founder of structural set theory—and Rosebrugh use the first one ("With one collection of morphisms") in the only book about structural set theory? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

3 2

Lectures by George Janelidze and workshop in Louvain-la-Neuve
by Tim Van der Linden 25 Feb '17

25 Feb '17

Dear Colleagues, We are very pleased to remind you that this May, Professor George Janelidze will be the recipient of the prestigious Chaire de la Vallee Poussin 2017 (see http://www.uclouvain.be/784661.html) at the Universite catholique de Louvain. On this occasion, professor Janelidze will give a series of invited lectures entitled "From Galois theory to commutative Hopf algebras and finite topological spaces". Abstract: These lectures are about Galois theory, which begins with field extensions, makes several steps of wide generalization, and eventually arrives at a purely category-theoretic level, where it gets new motivation and many new expected and unexpected examples. These examples will be described, with special remarks on commutative Hopf algebras that appear as Galois groups, and the whole last lecture devoted to algebraic topology of finite spaces, where the Galois theory of covering spaces works especially well. Schedule: Tuesday, May 30, 16:30: "Evolution of Galois theory" Wednesday, May 31, 11:00: "Categorical foundation" Wednesday, May 31, 16:30: "Concrete Galois theories" Thursday, June 1, 10:00: "Algebraic topology of finite spaces" -------------------------------------------------------------- A Workshop on Categorical Methods in Non-Abelian Algebra will follow from June 1st to 3rd, 2017. Please, let us know as soon as possible if you want to participate by sending a message to tim.vanderlinden(a)uclouvain.be. Participants are warmly invited to present talks. The deadline for registration and abstract submission is April 30, 2017. Further information can be found at the workshop webpage: http://www.mat.uc.pt/~mmc/mcana/MCANAfifthworkshop.html Looking forward to seeing you in Louvain-la-Neuve, The organizers Alan Cigoli Maria Manuel Clementino Marino Gran Tim Van der Linden Joost Vercruysse Enrico Vitale [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

LOLA 2017: Call for Talk Proposals
by Noam Zeilberger 25 Feb '17

25 Feb '17

The following workshop may be of interest to some readers of this list. ################## CALL FOR TALK PROPOSALS LOLA 2017: Syntax and Semantics of Low-Level Languages ====================================================== Monday, 19 June 2017, Reykjavik, Iceland A satellite workshop of LICS 2017 http://events.cs.bham.ac.uk/lola2017/ Important Dates --------------- - Abstract submission: Wednesday, 19 April 2017 - Author notification: Monday, 1 May 2017 - Workshop: Monday, 19 June 2017 Invited Speakers ---------------- - TBD Context ------- Since the late 1960s it has been known that tools and structures arising in mathematical logic and proof theory can usefully be applied to the design of high-level programming languages, and to the development of reasoning principles for such languages. Yet low-level languages, such as machine code, and the compilation of high-level languages into low-level ones have traditionally been seen as having little or no essential connection to logic. However, a fundamental discovery of this past decade has been that low-level languages are also governed by logical principles. From this key observation has emerged an active and fascinating new research area at the frontier of logic and computer science. The practically- motivated design of logics reflecting the structure of low-level languages (such as heaps, registers and code pointers) and low-level properties of programs (such as resource usage) goes hand in hand with some of the most advanced contemporary research in semantics and proof theory, including classical realizability and forcing, double orthogonality, parametricity, linear logic, game semantics, uniformity, categorical semantics, explicit substitutions, abstract machines, implicit complexity and resource bounded programming. The LOLA workshop, affiliated with LICS 2017, will bring together researchers interested in the relationships and connections between logic and low-level languages and programs. Topics of interest include, but are not limited to: - Typed assembly languages - Certified assembly programming - Certified and certifying compilation - Relaxed memory models - Proof-carrying code - Program optimization - Modal logic and realizability in machine code - Realizability and double orthogonality in assembly code - Parametricity, modules and existential types - General references, Kripke models and recursive types - Continuations and concurrency - Resource analysis and implicit complexity - Closures and explicit substitutions - Linear logic and separation logic - Game semantics, abstract machines and hardware synthesis - Monoidal and premonoidal categories, traces and effects Submission ---------- LOLA is an informal workshop aiming at a high degree of useful interaction amongst the participants, welcoming proposals for talks on work in progress, overviews of larger research programs, position presentations, and short tutorials, as well as more traditional research talks describing new results. The program committee will select the workshop presentations from submitted talk proposals, which may take the form either of a *two page abstract* or of a longer (published or unpublished) paper describing completed work. Authors are invited to submit their contribution by April 28, 2017. Abstracts must be written in English and be submitted as a single PDF file at [EasyChair](https://www.easychair.org/conferences/?conf=lola2017). Submissions will undergo a lightweight review process and will be judged on originality, relevance, interest and clarity. Submission should describe novel works or works that have already appeared elsewhere but that can stimulate the discussion between different communities at the workshop. The workshop will not have formal proceedings and is not intended to preclude later publication at another venue. Program Committee ----------------- - Beniamino Accattoli, INRIA - Michael Greenberg, Pomona College - Patricia Johann, Appalachian State University - Ohad Kammar, University of Oxford - Matija Pretnar, University of Ljubljana (co-chair) - Nikos Tzevelekos, Queen Mary University of London - Noam Zeilberger, University of Birmingham (co-chair) [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0

Re: Weighted limits
by Ross Street 21 Feb '17

21 Feb '17

Dear Jean On 15 Feb 2017, at 4:47 PM, Jean Benabou <jean.benabou(a)wanadoo.fr<mailto:jean.benabou@wanadoo.fr>> wrote: However they both say that if S is a category with finite limits the 2-category Cat(S) is what I called strictly finitely 2-complete. I doubt it. Could they, or anybody else, tell me how yo prove Cat(S) has strict inverters? The type of limit of which you speak for 2-categories are those of ordinary enriched category theory with base Cat. First agree that Cat(S) has terminal object, pullbacks and cotensoring with the arrow category Arr (usually called blackboard bold 2). Next construct the category Iso with two objects and an isomorphism between them using finite colimits in Cat: take the pushout of the two functors 2 --> Arr which are bijective on objects to obtain the category with two objects and an arrow each way; then force the arrows to be inverse to each other using two coequalizers. This tells us how to obtain the cotensor {Iso, A} of Iso with any A in Cat(S) by a pullback and two equalizers. Now take a 2-cell t between two morphisms f, g : A --> B in Cat(S). It corresponds to an morphism t' : A --> {Arr, B} in Cat(S). The inverter of the 2-cell t is the pullback of the restriction morphism {Iso, B} --> {Arr, B} along t' : A --> {Arr, B}. These things go back to my paper 10. Limits indexed by category-valued 2-functors, J. Pure Appl. Algebra 8 (1976) 149--181; MR53#5695. (Now I prefer the term weighted limit to indexed limit.) For any nice base for enrichment, all weighted limits can be obtained from products, equalizers and cotensoring. In the case of Cat, cotensoring with Arr suffices. Best wishes, Ross [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

2 1

None
by Jean Benabou 17 Feb '17

17 Feb '17

Dear Steve, I can understand you don't like my question. Some of the answers I received prove that other mathematicians I respect approve of it, have thought about, and have given partial answers to it. If you have any objections, take a stand and give MATHEMATICAL reasons for your objections. All you say is; > I'm saying the same can happen in mathematics. Prove that it DID happen in my question! By the way, I'm no zoologist but, by fishing through your mails, I found a big gap in your refutation. Neither in your mails nor in Fred's did I find any reference to the octopus. If there is any good reason for this omission, mathematical OR zoological, please make it public and justify it. All the best, Jean Le 14 févr. 17 à 09:48, Steve Vickers a écrit : > Dear Fred, > > A good answer, but my point was that it was a bad question. > > You see this once you start pressing at the details. Are seals and > turtles fish? No, but on your definition it depends on whether > flippers count as legs or not. What about sea snakes? Obviously not > - they're snakes, that just happen to live in the sea. But then eels > do seem a bit more fishy. > > A meticulous zoologist would start piling on the subclauses to pin > it down more precisely, but we know that that does not actually > refine our understanding of zoology. It just amplifies the > misconceptions underlying the original question. > > > > All the best, > > Steve. > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]

1 0