Subject: Re: graphs ad spaces Date: Sat, 06 Feb 93 21:32:04 PST From: pratt@CS.Stanford.EDU From: "Allen Knutson" Date: Thu, 28 Jan 93 19:31:28 EST > Whereas an edge is a subobject, an open set is a congruence class. Mm? I would've called a closed set a congruence class - putting on an equivalence relation should be like taking a (Hausdorff) quotient, which unifies a closed subset, not an open one. So I still think open sets are a red herring for your purposes. Not at all. The distinction between open and closed sets is "static" in the sense that it applies only to the objects of Top, not their morphisms. That the inverse image of a continuous function takes open sets to open implies that it takes closed sets to closed, *and conversely*. The generalization from topological spaces (T,O) to hyperspaces (T,O) (still a set of *points* paired with a set of its subsets called the *open sets*), obtained by dropping the requirement that unions and finite intersections of opens are open, removes even the static distinction. It is then quite arbitrary whether one calls the distinguished subsets of a hyperspace open or closed. I chose the former, but I'm open to arguments for calling them closed. This symmetry of open and closed does not obtain for hypergraphs (V,E), whose objects are as for hyperspaces (but now viewed as a set of *vertices* paired with a set of its subsets called the *edges*) but whose morphisms f:V->V' are such that the *direct* image of an edge in E is an edge in E'. This does not imply that the direct image of the complement of an edge is the complement of an edge. Whereas both inverse and direct images are complete semilattice maps, the inverse image preserves complements (i.e. is a CABA map) while the direct image instead preserves atoms. It is the preservation of complements that gives both open and closed sets the characteristics of a congruence class. The preservation of atoms makes edges look instead like subalgebras, but it does not make complements of edges look like subalgebras. This is a crucial difference between edges and open sets. -- Vaughan Pratt ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: ideals in additive categories Date: Wed, 10 Feb 93 21:49:12 -0500 From: "Allan Adler" Let C be an additive category. For every pair X,Y of objects of C, let A(X,Y) be a subgroup of the additive group Hom(X,Y). Assume that for every quadruple W,X,Y,Z of objects of C, we have Hom(W,X)xA(X,Y)xHom(Y,Z) --> Hom(W,Z) (by composition ) maps into A(W,Z). That seems like having an ideal and it seems like I should then be able to form a category in which the set of morphisms from an object X to an object Y is Hom(X,Y)/A(X,Y). Is there a name for such a system A and is there a name for the construction of modding out by A? Where is this formalized? Allan Adler ara@altdorf.ai.mit.edu ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: Re: ideals in additive categories Date: Mon, 15 Feb 93 16:47:50 CET From: max kelly see "On the radical of a category" by G.M.Kelly, J.Austral.Math.Soc.(?), around 1962. Max Kelly. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: Re: ideals in additive categories Date: Mon, 15 Feb 93 11:35:33 From: sjv@doc.ic.ac.uk (Steve Vickers) > Let C be an additive category. For every pair X,Y of objects of C, > let A(X,Y) be a subgroup of the additive group Hom(X,Y). Assume > that for every quadruple W,X,Y,Z of objects of C, we have > Hom(W,X)xA(X,Y)xHom(Y,Z) --> Hom(W,Z) (by composition ) maps into > A(W,Z). That seems like having an ideal and it seems like > I should then be able to form a category in which the set of > morphisms from an object X to an object Y is Hom(X,Y)/A(X,Y). > > Is there a name for such a system A and is there a name for > the construction of modding out by A? Where is this formalized? > > Allan Adler (I assume by "additive category" you just mean Abelian-group-enriched category. These are sometimes called "ringoids" on the analogy of the generalization from groups to groupoids.) This is just the start of a well-known theory of ringoids whose basic message is that they behave very much like non-commutative rings. I'd call the systems A you refer to just ideals. The main reference is Barry Mitchell's "Rings with several objects", pp. 1-161 in Advances in Mathematics 8 (1972), and I'm sure you'd find the construction there. I haven't checked, but it's conceivable it's also in N. Popescu's "Abelian categories with applications to rings and modules" (LMS Monographs 3, Academic Press, London, 1973). There is also a discussion and some results in my thesis. Incidentally, one way of viewing the theory is that it says that modules and homomorphisms are "really" just functors and natural transformations (and I guess that's what you see in Kelly's book on enriched categories). However, I've also found it helpful to see it the other way round: even in the non-additive context, it lets you see some functors (specifically functors to Sets, e.g. presheaves) and natural transformations as modules and homomorphisms, and that's helpful in understanding tensor products of functors, flatness, etc. In "Quantales, observational logic and process semantics", with Samson Abramsky (shortly to appear in Mathematical Structures in Computer Science), we used "quantaloids", or sup-lattice enriched categories, and there are similar results there. A good book about how to treat categories as algebras (though it doesn't cover the additive case) is Philip Higgins' "Notes on categories and groupoids" (Van Nostrand Reinhold, London, 1971). Steve Vickers. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: ftp sites Date: 22 Feb 93 14:23:15 EDT From: Charles Wells Has anyone compiled a list of papers related to category theory available by ftp? If not, I am willing to keep such a list if everyone will send me the locations where the papers are. It would be useful if you sent the ftp address, the directories where papers related to category theory are, and the names of any files in those directories that describe the papers therein. Any suggestions about better ways to do this are welcome. Charles Wells Department of Mathematics Case Western Reserve University 10900 Euclid Avenue Cleveland, OH 44106-7058 216-368-2893 -- Charles Wells Department of Mathematics, Case Western Reserve University University Circle, Cleveland, OH 44106-7058, USA 216 368 2893 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: my new address Date: Tue, 23 Feb 93 11:15:04 EST From: cbj@socs.uts.EDU.AU I've left Edinburgh for a permanent position in Sydney, Australia. Please send any correspondence to: Dr C. Barry Jay (Computing Methods Unit) School of Computing Sciences University of Technology, Sydney PO Box 123 Broadway NSW 2007 Australia phone: ++(61)(2) 330-1814 e-mail: cbj@socs.uts.edu.au Barry Jay ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: Re: ftp sites From: Paul Taylor Date: Tue, 23 Feb 1993 17:20:59 +0000 FTP sites - directory & mirroring Charles Wells asked earlier whether anyone has a list of ftp sites containing category theory papers, and offered to maintain one. It is possible to do better than this, and "mirror" the files, ie copy them automatically. Lee McLoughlin, who maintains an archive of general software in my department, SRC.doc.ic.ac.uk has written a program to do this, available as /packages/mirror/mirror.shar from there. [Please note that this is NOT the same archive as contains papers by my colleagues in the Theory & Formal Methods section and my TeX macros: that is THEORY.doc.ic.ac.uk] All that is needed is to collect the relevant information in an appropriate form. I suggest that this is also a good place to keep address information in a machine readable format. My entry in this database reads: package=TaylorP comment=Papers by Paul Taylor at Imperial site=theory.doc.ic.ac.uk remote_dir=/theory/papers/Taylor local_dir=TaylorP # email= # phone=+44 71 589 5111 x 5057 # fax=+44 71 581 8024 # address=Dept of Computing, Imperial College, London SW7 2BZ, UK This is to be found in the file /theory/papers/mirror-file in the theory archive. This file forms part of the configuration data needed by mirror; other sites should provide similar files. It would be possible, I suppose, for me to extract this information for other sites by searching my "categories" and "types" mail from past years and exploring the various ftp archives, but I consider this is something that sites should do for themselves. So, if you use an ftp archive for your papers, please compile an entry in the above format, and put it together with the other files for the users of the same archive in an appropriate place. Then mail me either the file itself or a pointer to it in the archive. I will then keep these files in the directory /theory/FTP-sites on my archive, for general use, as well as using them to mirror your files on a weekly basis. B U T This will only work if people are organised about the maintainance of their archives. In particular, there should be one directory(-tree) per person. Don't mix files by several authors in the same directory. This will be a very useful resource if we just put in a little bit of work to set it up. Paul Taylor ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Subject: Structures Directory Date: Tue, 23 Feb 93 13:26:33 AST From: Vaughan Pratt Time to post a fresh copy of the structures directory. Please let me know of corrections and additions (are there people you know that you think should be in this directory?) Vaughan Pratt # Structures Directory -- Email addresses of structure theorists # Release 4.0, February 23, 1993 # Master copy: Boole.Stanford.EDU:^ftp/pub/structdir # Maintainer: Vaughan Pratt, pratt@cs.stanford.edu # # # This is an email directory of logicians, algebraists, and programming # linguists working primarily on structural problems in mathematics and # computer science. It is organized as a Unix aliases file and # may be appended directly to the aliases file that normally resides in # /usr/lib or /etc. The most recent release of this directory may be # obtained at any time by anonymous ftp from Boole.Stanford.EDU as the # file /pub/structdir # # The purpose of this directory is to permit those listed in it to be # easily contacted individually by email. # # NOTICE: Please do not use any email address obtained from this # directory for other than the purpose stated above without first # obtaining the consent of the owner of that address. Such proscribed # uses include adding an address obtained from this directory to a # mailing list used for broadcast mailings, and noting the fact of # inclusion in this directory in a profile of the included individual. # # The list observes the following conventions. Column 1 is the alias, # which usually consists of the surname prefixed when necessary for # disambiguation with an initial or the whole first name. It starts in # character column 1 and is restricted to the 26 characters a-z (no # capitals, digits, or punctuation), and usually includes any preceding # "de" or "van". Column 2, which starts in character column 17, is the # email address in lower case with no %'s, and is either a regular # internet domain address, a .bitnet address, or a uucp address in ! # format. Column 3 is "(Forename" and column 4 the matching "Surname)". # The list is sorted by surname using the Unix sort command in the form # `sort +3` (sort ignoring the first three columns). The "de" or "van" # if any is placed in whichever of columnn 3 or 4 achieves its owner's # preferred alphabetization. Column 3 starts as close to column 57 as # possible subject to the other constraints and column 4 is separated # from column 3 by one space. There are no tabs in the file, and no line # is longer than 79 characters. # # Although the directory contains no repeated aliases (column 1 entries), # the aliases file to which you append it may already contain aliases # that also appear here. You should be aware that the resulting # conflicts will not be reported as such, but rather that the mailing # programs will select either the last or first repeated alias as the one # to use depending respectively on whether or not your mail system # preprocesses the aliases file for faster retrieval. # # Vaughan Pratt # Computer Science Department # Stanford University # Stanford, CA 94305 # pratt@cs.stanford.edu # 415-723-2943 abadi: ma@src.dec.com (Martin Abadi) abiteboul: abitebou@inria.inria.fr (Serge Abiteboul) abramsky: sa@doc.ic.ac.uk (Samson Abramsky) aceto: luca@cogs.sussex.ac.uk (Luca Aceto) aczel: petera@cs.man.ac.uk (Peter Aczel) adamek: adamek@unipas.fmi.uni-passau.de (Jiri Adamek) adams: useradms@mtsg.ubc.ca (Bob Adams) adelman: murray@macadam.mpce.mq.edu.au (Murray Adelman) adler: ara@lom1.math.yale.edu (Alan Adler) ait-kaci: hak@decprl.dec.com (Hassan Ait-Kaci) aitchison: iain@mundoe.munnari.oz.au (Iain Aitchison) altenkirch: alti@dcs.ed.ac.uk (Thorsten Altenkirch) amadio: amadio@dmi.ens.fr (Roberto Amadio) ambler: sja@dcs.qmw.ac.uk (Simon Ambler) anderson: anderson@bright.math.uoregon.edu (Frank Anderson) andreka: h2644and@ella.hu (Hajnal Andreka) apt: apt@cs.utexas.edu (Krzystof Apt) arnold: arnold@geocub.greco-prog.fr (Andre Arnold) (artemov: art@log.mian.su Sergei Artemov) artemov: sergei@artemov.mian.su (Sergei Artemov) asperti: andrea.asperti@inria.fr (Andrea Asperti) astesiano: astes@igecuniv.bitnet (Egidio Astesiano.) atkinson: atkinson@math.toronto.edu (Derek Atkinson) avron: aa@math.tau.ac.il (Arnon Avron) bach: rene@tech.ascom.ch (Rene Bach) baker: kab@math.ucla.edu (Kirby Baker) baranoff: sergei@hm.iias.spb.su (Sergei Baranoff) barr: barr@triples.math.mcgill.ca (Michael Barr) bartle: rgb@math.ams.com (Bob Bartle) barwise: barwise@phil.indiana.edu (Jon Barwise) beck: beck@mssun7.msi.cornell.edu (Jon Beck) beeson: beeson@ucscc.ucsc.edu (Michael Beeson) beigel: beigel-richard@cs.yale.edu (Richard Beigel) bellin: glb@dcs.edinburgh.ac.uk (Gian-Luigi Bellin) benson: dbenson@eecs.wsu.edu (David Benson) vanbenthem: johan@fwi.uva.nl (Johan.van Benthem) bergman: gbergman@cartan.berkeley.edu (George Bergman) bergstra: madelon@fwi.uva.nl (Jan Bergstra) berry: berry@cma.cma.fr (Gerard Berry) betti: betti@unimat.to.cnr.it (Renato Betti) bhadhuri: pbhaduri@cs2.cs.wsu.edu (Purandar Bhadhuri) bier: eric_bier.parc@xerox.com (Eric Bier) birtwistle: graham@cpsc.ucalgary.ca (Graham Birtwistle) blair: ziggy@hx.lcs.mit.edu (Michael Blair) blass: blass@um.cc.umich.edu (Andreas Blass) bbloom: bard@cs.cornell.edu (Bard Bloom) sbloom: bloom@sparc1.stevens-tech.edu (Steve Bloom) lblum: lblum@ernie.berkeley.edu (Lenore Blum) mblum: blum@ernie.berkeley.edu (Manuel Blum) blute: blute@triples.math.mcgill.ca (Richard Blute) vanemdeboas: pveb@cwi.nl (Peter.van.Emde Boas) boehm: boehm.pa@xerox.com (Hans Boehm) bonacina: bonacina@sbcs.sunysb.edu (M.Paola Bonacina) boolos: boolos@athena.mit.edu (George Boolos) borceux: fborceux@buclln11.bitnet (Francis Borceux.) jborwein: jborwein@cs.dal.ca (Jon Borwein) pborwein: pborwein@cs.dal.ca (Peter Borwein) bouchard: eomsg@acadvm1.uottawa.ca (Monique Bouchard) boyer: boyer@cli.com (Bob Boyer) bracho: bracho@unamvm1.bitnet (Felipe Bracho) breazu: val@linc.cis.upenn.edu (Val Breazu-Tannen) tannen: val@cis.upenn.edu (Val Breazu-Tannen) breen: math.univ-paris13.fr (Larry Breen) brink: cbrink@ucthpx.uct.ac.za (Chris Brink) brinkman: mabrink@dknkurz1.bitnet (Hans-Berndt Brinkman.) britz: brtkat01@ucthpx.uct.ac.za (Katarina Britz) brookes: brookes@b.gp.cs.cmu.edu (Steve Brookes) cbrown: cbrown@cs.chalmers.se (Carolyn Brown) rbrown: r.brown@vaxa.bangor.ac.uk (Ronnie Brown) broy: broy@lan.informatik.tu-muenchen.dbp.de (Manfred Broy) bruce: kim@cs.williams.edu (Kim Bruce) brunner: hbrunner@mun.bitnet (Herman Brunner) debukh: ecomail@vms2.uni-c.dk (Per.de Bukh) bullejos: mbullejos@ugr.es (Manuel Bullejos) buneman: peter@cis.upenn.edu (Peter Buneman) bunge: bunge@triples.math.mcgill.ca (Marta Bunge) burroni: burroni@mathp7.jussieu.fr (Albert Burroni) burstall: rb@dcs.edinburgh.ac.uk (Rod Burstall) buss: sbuss@cs.ucsd.edu (Sam Buss) cannon: cannon_j@maths.su.oz.au (John Cannon) carboni: carboni@imiucca.unimi.it (Aurelio Carboni) cardelli: luca@src.dec.com (Luca Cardelli) carpenter: carp@lcl.cmu.edu (Bob Carpenter) carr: carrdm@snyplaba.bitnet (Donna Carr) carter: nicola@mcgill1.bitnet (Nicola Carter) cartwright: cork@rice.edu (Corky Cartwright) casley: casley@cs.stanford.edu (Ross Casley) castellini: g-castellini@upr1.upr.cun.edu (G. Castellini) chandra: ashok@watson.ibm.com (Ashok Chandra) chen: chen@pchu.depaul.edu (Andy Chen) choi: choi@grad1.cis.upenn.edu (Jin-Young Choi) chou: chou@rascal.ics.utexas.edu (Shang-Ching Chou) chu: chu@ace.bsd.uchicago.edu (Po-Hsiang Chu) clarke: clarke@a.cs.cmu.edu (Ed Clarke) clote: clote@bcuxs2.bc.edu (Peter Clote) cockett: robin@cpsc.ucalgary.ca (Robin Cockett) cocquand: coquande@margaux.inria.fr (Thierry Cocquand) cohen: avrac@computer-lab.cambridge.ac.uk (Avra Cohen) comer: comers@citadel.bitnet (Stephen Comer) cooper: cooper@cogsci.edinburgh.ac.uk (Robin Cooper) cosmadakis: stavros@saul.cis.upenn.edu (Stavros Cosmadakis) cowen: mthmjc@ubvms.bitnet (Mike Cowen) crans: crans@math.ruu.nl (Sjoerd Crans) crew: crew@cs.stanford.edu (Roger Crew) crole: rlc@doc.imperial.ac.uk (Roy Crole) crossley: jnc@bruce.cs.monash.oz.au (John Crossley) crow: crow@csl.sri.com (Judy Crow) cruciani: cruciani@vaxrma.infn.it (Rosanna Cruciani) cubric: cubric@triples.math.mcgill.ca (Djordje Cubric) curien: curien@dmi.ens.fr (Pierre-Louis Curien) davey: davey@latcs1.lat.oz.au (Brian Davey) davis: davism@acf4.nyu.edu (Martin Davis) dawson: rdawson@husky1.stmarys.ca (Robert Dawson) degano: degano@di.unipi.it (Pier-Paolo Degano) delfour: delfour@cc.umontreal.ca (Michel Delfour) diaconescu: rdcbb@cunyvm.bitnet (Radu Diaconescu) diekert: diekert@informatik.tu-muenchen.dbp.de (Volker Diekert) diers: diers@frcitl81.bitnet (Yves Diers) doh: doh@ksuvax1.cis.ksu.edu (Kyung-Goo Doh) dolan: v088kj6a@ubvms.cc.buffalo.edu (James Dolan) doob: mdoob@ccu.umanitoba.ca (Michael Doob) dragalin: h2848dra@ella.hu (? Dragalin) duba: duba@rice.edu (Bruce Duba) dubey: rdubey@yoda.eecs.wsu.edu (Rakesh Dubey) dubuc: dcfden!edubuc@mate.edu.ar (Eduardo Dubuc) duggan: den@cs.umd.edu (Dominic Duggan) dunn: dunn@iuvax.cs.indiana.edu (Mike Dunn) duskin: mthduskn@ubvms.bitnet (Jack Duskin) dybkjaer: dybkjaer@diku.dk (Hans Dybkjaer) edalat: ae@doc.ic.ac.uk (Abbas Edalat) ehlers: map010@bangor.ac.uk (Philip Ehlers) ehresmann: ehres@mathp7.jussieu.fr (Andree Ehresmann) ehrhard: ehrhard@ens.fr (Thomas Ehrhard) ehrlich: ehrlich@inria.inria.fr (Bobby Ehrlich) vaneijck: jve@cwi.nl (Jan.van Eijck) emerson: a.emerson@cs.utexas.edu (Alan Emerson) enderton: hbe@math.ucla.edu (Herb Enderton) engeler: engeler@math.ethz.ch (Erwin Engeler) ernst: mernst@theory.lcs.mit.edu (Michael Ernst) fagin: fagin@almaden.ibm.com (Ron Fagin) faro: v068p76v@ubvmsa.bitnet (Emilio Faro) fasel: jhf@lanl.gov (Joe Fasel) feferman: sf@csli.stanford.edu (Sol Feferman) feigenbaum: jf@research.att.com (Joan Feigenbaum) feldman: d_feldman@unhh.bitnet (David Feldman) ferguson: mike@tel.inrs.cdn (Michael Ferguson) finkelstein: stacy@saul.cis.upenn.edu (Stacy Finkelstein) fischer: fischer-michael@cs.yale.edu (Mike Fischer) fitting: mlflc@cunyvm.bitnet (Melvin Fitting) floyd: floyd@cs.stanford.edu (Bob Floyd) foo: norman@cs.su.oz.au (Norman Foo) fourman: mikef@dcs.edinburgh.ac.uk (Michael Fourman) fox: fox@triples.math.mcgill.ca (Thomas Fox) freese: ralph@kahuna.math.hawaii.edu (Ralph Freese) frei: bitnet.arfr@ubcmtsg (Armin Frei) freire: freire@seins.santiago.usc.es (J.L. Freire) freyd: pjf@linc.cis.upenn.edu (Peter Freyd) pamfreyd: pam@linc.cis.upenn.edu (Pam Freyd) fritsch: rudolf.fritsch@mathematik.uni-muenchen.dbp.de (Rudolph Fritsch) gago: alzzs002@seins.santiago.usc.es (Felipe Gago) gaifman: gaifman@humus.huji.ac.il (Haim Gaifman) gallier: jean@saul.cis.upenn.edu (Jean Gallier) ganong: ganong@vm1.yorku.ca (Richard Ganong) vangelder: avg@cs.ucsc.edu (Allen.Van Gelder) genrich: genrich@gmdzi.gmd.de (Hartmann Genrich) geramita: anthony.v.geramita@queensu.ca (Anthony Geramita) gerstenhaber: gersten@penndrls.bitnet (Murray Gerstenhaber) gerth: wsinrobg@eutrc3.urc.tue.nl (Rob Gerth) ghelli: ghelli@di.unipi.it (Giorgio Ghelli) girard: girard@margaux.inria.fr (Jean-Yves Girard) givant: givant@mills.berkeley.edu (Steve Givant) vanglabbeek: rvg@cs.stanford.edu (Rob.van Glabbeek) goguen: joseph.goguen@prg.oxford.ac.uk (Joseph Goguen) bgoldberg: goldberg@cs.nyu.edu (Ben Goldberg) goldblatt: rob@math.vuw.ac.nz (Rob Goldblatt) goltz: gf1018@dbngmd21.bitnet (Ulla Goltz) goodaire: edgar@munucs.mun.ca (Edgar Goodaire) gordon: v5200e@templevm.bitnet (Bob Gordon.) grandis: grandis@igecuniv.bitnet (Marco Grandis.) gratzer: gratzer@ccm.umanitoba.ca (George Gratzer) gray: gray@math.uiuc.edu (John Gray) grove: grove@cs.stanford.edu (Adam Grove) gruska: gruska@rosun1.informatik.uni-hamburg.de (Jozef Gruska) guessarian: ig@litp.ibp.fr (Irene Guessarian) guitart: guitart@mathp7.jussieu.fr (Rene Guitart) gunawardena: jhcg@hplb.hpl.hp.com (Jeremy Gunawardena) cgunter: gunter@central.cis.upenn.edu (Carl Gunter) egunter: elsa@research.att.com (Elsa Gunter) gupta: vgupta@cs.stanford.edu (Vineet Gupta) gurevich: gurevich@dip.eecs.umich.edu (Yuri Gurevich) dhalpern: jdan@sun.com (Dan Halpern) jhalpern: halpern@almaden.ibm.com (Joe Halpern) hanna: fkh@ukc.ac.uk (Keith Hanna) hardie: hardieka@uctvax.uct.ac.za (Kieth Hardie) harel: harel@wisdom.weizmann.ac.il (David Harel) harland: jah@mullauna.cs.mu.oz.au (James Harland) harper: rwh@proof.ergo.cs.cmu.edu (Robert Harper) hart: wiawkph@dutrun2.tudelft.nl (Klaas Hart) haveraaen: magne@eik.ii.uib.no (Magne Haveraaen) hebert: mhebert@mat.ulaval.ca (Michel Hebert) heckmann: heckmann@cs.uni-sb.de (Reinhold Heckmann) heggie: heggie@cad.uccb.ns.ca (Murray Heggie) hennessy: matthewh@cogs.sussex.ac.uk (Matthew Hennessy) henriksen: henriksen@hmcvax.claremont.edu (Mel Henriksen) henzinger: tah@cs.stanford.edu (Tom Henzinger) herz: herz@gauss.math.mcgill.ca (Carl Herz) hill: whill@hplwlh.hpl.hp.com (Walt Hill) hillebrand: ggh@cs.brown.edu (Gerd Hillebrand) hindley: majrh@pyr.swan.ac.uk (Roger Hindley) hoare: julie@prg.oxford.ac.uk (Tony Hoare) hodgson: bhodgson@vm1.ulaval.ca (Bernard Hodgson) hoehnke: gabi@opal.cs.tu-berlin.de (Hans-Jurgen Hoehnke) honsell: honsell@uduniv.cineca.it (Furio Honsell) hoofman: raymond@cs.ruu.nl (Raymond Hoofman) hook: hook@cse.ogi.edu (James Hook) hopcroft: jeh@cs.cornell.edu (John Hopcroft) hsiang: hsiang@sbcs.sunysb.edu (Jieh Hsiang) hudak: hudak@cs.yale.edu (Paul Hudak) huet: huet@inria.inria.fr (Gerard Huet) hunsaker: ga3600@siucvmb.bitnet (W. Hunsaker) husberg: nhu@dione.hut.fi (Nisse Husberg) huth: mrh@tulmath.math.tulane.edu (Michael Huth) hyland: jmeh1@phoenix.cambridge.ac.uk (Martin Hyland) israel: israel@ai.sri.com (David Israel) istrail: sistrail@eagle.wesleyan.edu (Soren Istrail) ito: ito@ito.ecei.tohoku.junet (Takayasu Ito) iyer: ramu@cadsun.corp.mot.com (Ramu Iyer) jacobs: bjacobs@math.ruu.nl (Bart Jacobs) jaffar: joxan@watson.ibm.com (Joxan Jaffar) jagadeesan: rj2@doc.imperial.ac.uk (Radhakrishnan Jagadeesan) janssen: theo@fwi.uva.nl (Theo Janssen) jardine: jardine@uwovax.uwo.ca (John Jardine) jay: cbj@dcs.edinburgh.ac.uk (Barry Jay) jeffrey: alan.jeffrey@prg.oxford.ac.uk (Alan Jeffrey) jenkins: maj@qucis.bitnet (Mike Jenkins) mjohnson: mike@macadam.mpce.mq.edu.au (Mike Johnson) pjohnson: pjohnson@eagle.wesleyan.edu (Paul Johnson) jonsson: jonssob@vuctrvax.bitnet (Bjarni Jonsson.) jouvelot: jouvelot@ensmp.fr (Pierre Jouvelot) (joyal: joyal@math.uqam.ca AfterJun92:Andre Joyal) joyal: a.joyal@dpmms.cambridge.ac.uk (ToJun92:Andre Joyal) joyce: djoyce@ollie.clarku.edu (David Joyce) jung: jung@mathematik.th-darmstadt.de (Achim Jung) kahn: kahn@mirsa.inria.fr (Gilles Kahn) kane: kane@uwovax.uwo.ca (Richard Kane) kanellakis: pck@cs.brown.edu (Paris Kanellakis) kao: kao@iuvax.cs.indiana.edu (Ming Kao) kapranov: kapranov@mssun7.msi.cornell.edu (Mikhail Kapranov) karp: karp@ernie.berkeley.edu (Dick Karp) kasangian: kasan@imiucca.unimi.it (Stefano Kasangian) kelly: kelly_m@maths.su.oz.au (Max Kelly) kennaway: jrk@sys.uea.ac.uk (Richard Kennaway) kennison: jkennison@clarku (John Kennison) kfoury: kfoury@bu-cs.bu.edu (Dennis Kfoury) kiehn: kiehn@lan.informatik.tu-muenchen.dbp.de (Astrid Kiehn) klarlund: klarlund@cs.cornell.edu (Nils Klarlund) kleisli: kleisli@cfruni52.bitnet (Heinrich Kleisli.) klop: jwk@cwi.nl (Jan Klop) knijnenburg: peterk@cs.ruu.nl (Peter Knijnenburg) kochman: kochman@nexus.yorku.ca (Stanley Kochman) kock: matak@mi.aau.dk (Anders Kock) kolaitis: kolaitis@cs.ucsc.edu (Phokion Kolaitis) koslowski: koslowj@math.ksu.edu (Juergen Koslowski) kozen: kozen@cs.cornell.edu (Dexter Kozen) kwiatkowska: mzk@leicester.ac.uk (Marta Kwiatkowska) labute: labute@gauss.math.mcgill.ca (John Labute) ladkin: ladkin@icsib8.berkeley.edu (Peter Ladkin) ladner: ladner@cs.washington.edu (Richard Ladner) lafont: lafont@dmi.ens.fr (Yves Lafont) lamarche: lamarche@dmi.ens.fr (Francois Lamarche) lambe: lambe@math.ethz.ch (Larry Lambe) lambek: lambek@triples.math.mcgill.ca (Joachim Lambek) lampe: lampe@kahuna.math.hawaii.edu (Bill Lampe) lamport: lamport@src.dec.com (Leslie Lamport) lassez: jll@watson.ibm.com (Jean-Louis Lassez) latch: dml@bklyncis.bitnet (Dana Latch) launchbury: jl@dcs.glasgow.ac.uk (John Launchbury) lawvere: mthfwl@ubvmsb.cc.buffalo.edu (Bill Lawvere) leavens: leavens@bambam.cs.iastate.edu (Gary Leavens) leeney: stmt8015@iruccvax.ucc.ie (Mark Leeney) leivant: daniel.leivant@b.gp.cs.cmu.edu (Daniel Leivant) lent: aflent@theory.lcs.mit.edu (Arthur Lent) levin: lnd@cs.bu.edu (Leonid Levin) liao: aliao@eagle.wesleyan.edu (Andrew Liao) libkin: libkin@saul.cis.upenn.edu (Leonid Libkin) lifschitz: lifschitz@cs.stanford.edu (Vladimir Lifschitz) lilius: jli@dione.hut.fi (Johan Lilius) lincoln: lincoln@cs.stanford.edu (Pat Lincoln) linton: flinton@eagle.wesleyan.edu (Fred Linton) longo: longo@dmi.ens.fr (Giuseppe Longo) lord: hlord@csupomona.edu (Harriet Lord) loui: mloui@note.nsf.gov (Michael Loui) lowry: lowry@kestrel.edu (Mike Lowry) lubarsky: r_lubarsky@faudm.bitnet (Robert Lubarsky) lubliner: coby@ucbcevax.bitnet (Coby Lubliner) luckham: dcl@anna.stanford.edu (David Luckham) lynch: lynch@holmes.lcs.mit.edu (Nancy Lynch) ma: qingming.ma@cs.cmu.edu (Qingming Ma) macdonald: macstone@bdc.ubc.ca (John MacDonald) mackenzie: pm1kchm@primea.sheffield.ac.uk (K.Charles.H. 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Sankappanevar) sannella: dsannella@dcs.edinburgh.ac.uk (Don Sannella) saraswat: saraswat@parc.xerox.com (Vijay Saraswat) sato: schuko@sun4.cc.kyushu-u.ac.jp (Hiroyuki Sato) scedrov: andre@cis.upenn.edu (Andre Scedrov) schelter: wfs@cli.com (Bill Schelter) schmidt: jschmidt@daimi.dk (Jorn Schmidt) schroeppel: rcs@la.tis.com (Rich Schroeppel) schumacher: schu@acadia.bitnet (Dietmar Schumacher) scollo: scollo@cs.utwente.nl (Giuseppe Scollo) dscott: dscott@risc.uni-linz.ac.at (Dana Scott) pscott: pjs@dcs.ed.ac.uk (Phil Scott) seely: rags@triples.math.mcgill.ca (Robert Seely) seldin: seldin@alcor.concordia.ca (Jonathan Seldin) seligman: jerry@phil.indiana.edu (Jerry Seligman) shankar: shankar@csl.sri.com (Natarajan Shankar) shapiro: udi@wisdom.weizmann.ac.il (Udi Shapiro) shieber: shieber@das.harvard.edu (Stuart Shieber) shields: m.shields@mcs.surrey.ac.uk (Mike Shields) sichler: sichler@ccm.umanitoba.ca (Jiri Sichler) kurt: sieber@fb10vax.informatik.uni-saarland.dbp.de (Kurt Sieber) isimon: is@ime.usp.br (Imre Simon) simons: simons@karlsruhe.gmd.de (Martin Simons) slifker: slifker@svax.cs.cornell.edu (Michael Slifker) smaill: smaill@aipna.edinburgh.ac.uk (Alan Smaill) small: nwnexus!cjsa!jeff@uunet.uu.net (Jeffery Small) gsmith: dalcs!gretchen@uunet.uu.net (Gretchen Smith) ssmith: scott@cs.jhu.edu (Scott Smith) ssmolka: sas@cs.sunysb.edu (Scott Smolka) gsmolka: smolka@dfki.uni-sb.de (Gert Smolka) soare: soare@gargoyle.uchicago.edu (Bob Soare) sobral: sobral@ciuc2.uc.rccn.pt (Manuela Sobral) spencer: dwights@cse.ogi.edu (Dwight Spencer) spreen: spreen@hrz.uni-siegen.dbp.de (Dieter Spreen) srinivas: srinivas@madeleine.ics.uci.edu (Yellamraju Srinivas) staples: staples@uqcspe.cs.uq.oz.au (John Staples) stark: stark@cs.sunysb.edu (Eugene Stark) steele: steele@think.com (Guy Steele) steiner: maths@vme.gla.ac.uk (Richard Steiner) stell: john@cs.kl.ac.uk (John Stell) stewart: cstewart@watserv1.uwaterloo.ca (Cameron Stewart) stolboushkin: aps1@node.ias.msk.su (Alex Stolboushkin) astone: macstone@bdc.ubc.ca (Art Stone) stoughton: allen@cogs.sussex.ac.uk (Allen Stoughton) stout: lnstout@uxh.cso.uiuc.edu (Lawrence Stout) strecker: strecker@galois.math.ksu.edu (George Strecker) street: street@macadam.mpce.mq.edu.au (Ross Street) streicher: streiche@unipas.fmi.uni-passau.de (Thomas Streicher) subrahmanyam: ramesh@linc.cis.upenn.edu (Ramesh Subrahmanyam) sun: yong@minster.york.ac.uk (Yong Sun) suppes: suppes@csli.stanford.edu (Pat Suppes) swaminathan: swami@cs.dal.ca (S. Swaminathan) szabo: szabo@vax2.concordia.ca (Fred Szabo) takayama: takayama@okilab.oki.co.jp (Yukihide Takayama) talcott: clt@sail.stanford.edu (Carolyn Talcott) tatsuta: tatsuta@sato.riec.tohoku.ac.jp (Makoto Tatsuta) taubner: taubner@lan.informatik.tu-muenchen.dbp.de (Dirk Taubner) paultaylor: pt@doc.ic.ac.uk (Paul Taylor) philiptaylor: p.taylor@vax.rhbnc.ac.uk (Philip Taylor) wtaylor: wtaylor@boulder.colorado.edu (Walt Taylor) tennent: rdt@qucis.queensu.ca (Bob Tennent) thiagarajan: pst@ssf.ernet.in (P.S. Thiagarajan) tholen: tholen@vm1.yorku.ca (Walter Tholen) thomson: tom@nw.stl.stc.co.uk (Tom Thomson) thurston: wpt@math.princeton.edu (Bill Thurston) tierney: tierney@math.uqam.ca (Myles Tierney) tiuryn: tiuryn@cs.bu.edu (Jerzy Tiuryn) tonks: map003@vaxa.bangor.ac.uk (Andy Tonks) trakhtenbrot: trakhte@math.tau.ac.il (Boris Trakhtenbrot) trnkova: UMMVT@CSEARN.bitnet (Vera Trnkova) tschantz: tschantz@athena.cas.vanderbilt.edu (Steve Tschantz) tsuiki: tsuiki@kurims.kyoto-u.ac.jp (Hideki Tsuiki) turbak: lyn@zurich.ai.mit.edu (Franklyn Turbak) urquhart: urquhart@ai.toronto.edu (Alasdair Urquhart) valeriote: matt@johnny.math.mcmaster.ca (Matt Valeriote) vanosdol: d_vanosdol@unhh.unh.edu (Donovan Van.Osdol) vardi: vardi@almaden.ibm.com (Moshe Vardi) vermeulen: jjcvmath.uctvax@f4.n494.z5.fidonet.org (Japie Vermeulen) verwer: nico@cs.ruu.nl (Nico Verwer) vianu: vdvianu@ucsd.edu (Victor Vianu) vickers: sjv@doc.ic.ac.uk (Steve Vickers) vitanyi: paulv@cwi.nl (Paul Vitanyi) voevodsky: vladimir@math.harvard.edu (Vladimir Voevodsky) devries: ferjan@cwi.nl (Fer-jan.de Vries) waarts: orli@cs.stanford.edu (Orli Waarts) wachter: wachter@itd.nrl.navy.mil (Ralph Wachter) wadler: wadler@dcs.glasgow.ac.uk (Philip Wadler) wagner: wagner@watson.ibm.com (Eric Wagner) wallen: lw@prg.ox.ac.uk (Lincoln Wallen) walters: walters_b@maths.su.oz.au (Bob Walters) wand: wand@corwin.ccs.northeastern.edu (Mitchell Wand) wasilewska: anita@sbcs.sunysb.edu (Anita Wasilewska) wells: cfw2@po.cwru.edu (Charles Wells) wendt: wendt@cs.dal.ca (Michael Wendt) white: bwhite@inmet.inmet.com (Bill White) williams: ewilliam@kean.ucs.mun.ca (Ed Williams) winkler: winkler@csl.sri.com (Timothy Winkler) winskel: gwinskel@daimi.dk (Glynn Winskel) wirsing: wirsing@unipas.fmi.uni-passau.de (Martin Wirsing) wood: rjwood@cs.dal.ca (Richard Wood) wraith: gavinw@sussex.ac.uk (Gavin Wraith) wright: gpwsg@acadvm1.uottawa.ca (Graham Wright) wyler: wyler@cs.cmu.edu (Oswald Wyler) yardini: eyal@wisdom.weizmann.ac.il (Eyal Yardini) yarroll: piggy@gargoyle.uchicago.edu (La.Monte Yarroll) yetter: dyetter@math.ksu.edu (David Yetter) yoshida: yoshida@icot.or.jp (Kaoru Yoshida) yoshiki: yoshiki@etl.go.jp (Kinoshita Yoshiki) young: young@xx.lcs.mit.edu (Jonathan Young) zawadowski: warsaw@ccb.uib.es (Marek Zawadowski) zenith: zenith@ensmp.fr (Steven Zenith) zhang: gqz@caen.engin.umich.edu (G.Q. Zhang) zocco: dean.zocco@klb (Meg Zocco)