October 1994 - Categories - categories.org.au

Re: sub-structures of free structures
by Michael Barr 01 Nov '94

01 Nov '94

> > Date: Sun, 23 Oct 1994 15:35:43 +0000 (GMT) > From: "John G. Stell" <john(a)cs.keele.ac.uk> > > > What results of the form `A sub-X of a free X is free' are known? > I am aware of groups, magmas (= set with binary operation), and > modules over a principal ideal domain. I'd be interested to hear of > structures for which this is either known to be true, or examples > where it fails. > > John Stell > It is true for abelian groups, but is false for both monoids and commutative monoids. The free (commutative) monoid on one element x has a submonoid consisting of 1,x^3,x^5,x^6 and all x^n for n > 7 is not free. Throwing away 1, you get counter-examples for semigroups and commutative semigroups. By taking the free abelian group on this example, you get counter-examples for rings and commutative rings. I am sure that it is a fairly rare occurrence. Michael Barr

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subobjects of free objects
by Prof R. Brown 31 Oct '94

31 Oct '94

What results of the form `A sub-X of a free X is free' are known? I am aware of groups, magmas (= set with binary operation), and modules over a principal ideal domain. I'd be interested to hear of structures for which this is either known to be true, or examples where it fails. John Stell There are a lot of counterexamples examples in the topological case. There is also a lot of work on the profinite case (open subgroups of free profinite groups are free profinite). Brown and Hardy proved open subgroups of free topological groups are free topological (various k_{\omega} conditions used) (JLMS (2)10 (1975) 431-440).Sid Morris has a good survey in Categorical Topology (Proceedings Toledo 1983, ed HLBentley et al). I have a paper in Proc AMS 52 (1975) 433-441 giving examples of non projective closed subgroups of the free topological group on [a,b] (e.g. the subgroup generated by {a} and x^2 for x \in [a,b], has \pi_0 = Z_2, which is not free). Ronnie Brown Prof R. Brown Tel: +44 248 382474 School of Mathematics Fax: +44 248 355881 Dean St email: mas010(a)uk.ac.bangor University of Wales Bangor Gwynedd LL57 1UT UK

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are local homemorphism part of a factorization system
by Thomas Streicher 27 Oct '94

27 Oct '94

Does anyone know whether in the category Geom of toposes and geometric morphism the local homemorphisms form the mono part of a factorization system ? Or is that at least the case in the luff subcategory where one has only essential geomtric morphism whose leftmost adjoint preserves pullbacks. Has this latter category ever been srudied ? Thomas Streicher

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ANNOUNCE: XY-pic version 2.12 released...
by kris＠diku.dk 25 Oct '94

25 Oct '94

Dear category theorist, This is to announce yet another BUG FIX release of my DIAGRAM DRAWING PACKAGE, XY-pic: version 2.12. It fixes the following user visible bugs in version 2.11: * No conflict with `AMS-LaTeX' version 1.2 (SEE BELOW). * No conflict with Karl Berry's `eplain' (SEE BELOW). * Curves with explicit control are now right [Sjoerd Crans]. * Directional vectors no longer invalidate the Xy-state [Luc van Eycken]. * Tips on zero-sized turns no longer reversed [Jorge Almeida]. * Curves no longer overlap the surrounding text. * Numerous documentation fixes in the Reference Manual. * Short steep segments now placed correctly [thanks, Ross]. I am sorry to announce this very interim version which is necessary because of a change in an internal function of AMS-LaTeX [sic]. Thus ** PLEASE UPDATE TO VERSION 2.12 IF YOU USE AMS-LaTeX *** The release of the `real' version 3 (no longer in beta-test) is imminent so you need not update otherwise unless any of the other bugs have bothered you (or you desperately need one of the additions described below). There is ONE IMPORTANT CHANGE in the v3 extensions of this version: the \arrow command has been renamed to \ar in order to make diagrams more concise and avoid conflict with Karl Berry's `eplain', however, using the `v2' compatibility option will still define \arrow (as well as \stop and \merge that are also in conflict with existing names on some systems). - o - One extension and one feature have been added with this release: * \xyoption{cmtip} allows the use of arrow tips that resemble those of D. Knuth's Computer Modern and Computer Concrete fonts. * \xyoption{poly} supports drawing of regular polygons (by Ross Moore). Version 3 will also have a special input mode for `knots and links'. - o - Xy-pic can be retrieved by anonymous ftp from ftp.diku.dk : /diku/users/kris/TeX/ ftp.mpce.mq.edu.au : /pub/maths/TeX/ (see the README file as to the exact location below that), from CTAN : /tex-archive/macros/generic/diagrams/xypic and also through the World Wide Web (see below). - o - NEWS: there is now a World Wide Web HOME PAGE for Xy-pic in <URL: http://www.diku.dk/users/kris/Xy-pic.html> which includes pointers to the sources as well as some TUTORIAL PAPERS on Xy-pic: * K.Rose: Xy-pic and Notation for Categorical Diagrams. * R.Moore: Typesetting Neural Nets with Xy-pic. (for people without WWW access these are also available on the ftp servers in files xy/papers/ecct-94.ps and xy/papers/NeuralNets.ps). - o - In the hope that you will like the new things, Kristoffer Rose -- Kristoffer H{\o}gsbro ROSE <kris(a)diku.dk> DIKU, Universitetsparken 1, 2100 K{\o}benhavn {\O}, DANMARK Phones: +45 35321400 direct: +45 35321420 fax: +45 35321401 World Wide Web <URL: http://www.diku.dk/users/kris/>

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PSSL in Aarhus
by Jaap van Oosten 24 Oct '94

24 Oct '94

This is an announcement of the 56th PSSL, to be held in the weekend of 3-4 December, in Aarhus, Denmark. The announcement follows in Latex code. Please post this at your department! Jaap van Oosten \documentstyle[12pt,a4]{article} \pagestyle{empty} \nofiles \begin{document} \begin{center} {\Large\bf Announcement 56$^{\mbox{\small\bf th}}$ PSSL} \end{center} The 56$^{\mbox{\scriptsize th}}$ {\em Peripatetic Seminar on Sheaves and Logic} will be held in the weekend of 3 and 4 December at the University of Aarhus, Denmark. As usual, we welcome talks on topics in logic, category theory and related areas in mathematics and computer science. Please publicize this meeting amongst your colleagues. At the time of the meeting, Ieke Moerdijk is in Aarhus as a guest of the Mathematics Department. The meeting will be jointly sponsored by the Mathematics department and the research centre BRICS (Basic Research In Computer Science), so no fees are to be expected. There are two airports serving Aarhus: Tirstrup (Aarhus airport), which is about 50 kilometres from the city and has a good bus connection to it, and Billund, which lies about 100 kilometres from Aarhus and has connection by bus (directly) or bus to Vejle and train from there (in some instances, the latter connection is quicker). Further details, also about accomodation, will follow. As we try to arrange relatively cheap accomodation in student houses, it will be appreciated if attendants register as soon as possible. \medskip Return, preferably by email, to \begin{tabbing} aaaaaa\=aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\=\kill \> Jaap van Oosten, \> Tel.~++45-8942 3468\\ \> Datalogisk Afdeling, \> Fax ++45 8942 3255\\ \> Aarhus Universitet \> Email {\tt jvoosten(a)daimi.aau.dk} \\ \> Ny Munkegade, Bld.~540 \\ \> DK-8000 Aarhus C, Denmark \end{tabbing} We look forward to seeing you in Aarhus.\\ The local organizers, \begin{quote} \begin{tabbing} Anders Kock\qquad\qquad\qquad \= Sergei Soloviev \qquad\qquad \= Vladimiro Sassone\\ Claudio Hermida\> Jaap van Oosten \end{tabbing} \end{quote} \hrule\vskip3pt I would like to attend the 56th PSSL:\\ \\ Name\dotfill \\ Return Address\dotfill \\ \hbox{}\dotfill\\ email \dotfill \\ $\Box$ I wish to give a talk entitled \dotfill\\ of 20/30/45 minutes.\\ I wish to book accomodation from\dotfill to \dotfill \\ \end{document}

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sub-structures of free structures (
by John G. Stell 23 Oct '94

23 Oct '94

What results of the form `A sub-X of a free X is free' are known? I am aware of groups, magmas (= set with binary operation), and modules over a principal ideal domain. I'd be interested to hear of structures for which this is either known to be true, or examples where it fails. John Stell

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colimits of Hilbert spaces
by john baez 21 Oct '94

21 Oct '94

I'm interested in colimits in the category of Hilbert spaces with isometries as morphisms. Is there a good reference on when these exist? John Baez

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coherent locales
by Paul Johnson 20 Oct '94

20 Oct '94

Dear categories, In ``Stone spaces'', Johnstone notes that the assumption that every coherent locale is spatial is equivalent to the prime ideal theorem for distributive lattices. Is it generally agreed that the assumption that the spatial part of every coherent locale has coherent topology is also equivalent to the above two axioms? Cheer, PBJ.

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literature on graphical algebras?
by Frank Piessens 18 Oct '94

18 Oct '94

Can somebody give me references to literature on Burroni's graphical algebras? The only paper I know of is: "Algebres graphiques" (A. Burroni), Cahiers de Topologie et Geometrie Differentielle, XXII, 1981. Many thanks, Frank Piessens. Frank.Piessens(a)cs.kuleuven.ac.be

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new phone numbers for Sydney University
by Max Kelly 18 Oct '94

18 Oct '94

Will colleagues please note that the prefix 692 has been changed to 351; thus we have new university numbers: Max Kelly +61-2-351-3796 Bob Walters +61-2-351-2966 Shu-Hao Sun +61-2-351-4076 Fax +61-2-351-4534 Regards from Max Kelly

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