61. Fields Institute Audio - Bunge Covering Morphisms in topos theory Marta Bunge McGill University.This web presentation contains the audio of a lecture given at http://www.fields.utoronto.ca/audio/02-03/galois_and_hopf/bunge/

LECTURE AUDIO June 6, 2004 Home About Us Prizes and Honours People ... Search Covering Morphisms in Topos Theory Marta Bunge McGill University This web presentation contains the audio of a lecture given at the Fields Institute on September 23, 2002 as part of the Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories . RealPlayer 7 or later, or other software capable of playing streaming audio, is required. Start audio presentation

62. Sketches Of An Elephant: A Topos Theory Compendium (Oxford Logic Guides, 43 & 44 Buy Sketches of an Elephant A topos theory Compendium (Oxford Logic Guides, 43 44) by Peter T. Johnstone (Hardcover June 2003) from home at our online http://www.mathbook.com/a/Linear_Algebra/Sketches_of_an_Elephant_A_Topos_Theory_

For Age: 4 years and up LeapPad by LeapFrog At Amazon on 4-15-2003. More Info This talking book comes with an interactive ''magic pen'' that works like a hand-held computer mouse pointer. Children can opt to turn the paper pages and listen to the story read with different voices for each character. Or they can interrupt the read-aloud session to play with the magic pen (permanently attached with a wire). They can point the pen tip to any word on a page and hear it pronounced, or touch a picture and hear a sound effect (such as ''Strike one!'' for the baseball bat). Very similar to the popular Living Books computer games, this 10-by-11-inch book is more portable than a home computer. Stories in this set include Lil's Loose Tooth, Richard Scarry's Best Word Book Ever, and Winnie the Pooh in A Sweet Good Morning. The set also includes a paper piano keyboard and map and human anatomy games. Gail Hudson Batteries: 4 AAbatteries required. How to Prepare for the SAT II: Math Level IC by James J. Rizzuto (Paperback - March 2000) Visit Our Sites: Buy Law Books Top Quality Wrist Watches

63. Sheaves In Geometry And Logic: A First Introduction To Topos Theory (Universitex Buy Sheaves in Geometry and Logic A First Introduction to topos theory (Universitext)by S. Mac Lane, et al (Paperback April 1992) from home at our online http://www.mathbook.com/t/Topology/Sheaves_in_Geometry_and_Logic_A_First_Introdu

For Age: 4 years and up LeapPad by LeapFrog At Amazon on 4-15-2003. More Info This talking book comes with an interactive ''magic pen'' that works like a hand-held computer mouse pointer. Children can opt to turn the paper pages and listen to the story read with different voices for each character. Or they can interrupt the read-aloud session to play with the magic pen (permanently attached with a wire). They can point the pen tip to any word on a page and hear it pronounced, or touch a picture and hear a sound effect (such as ''Strike one!'' for the baseball bat). Very similar to the popular Living Books computer games, this 10-by-11-inch book is more portable than a home computer. Stories in this set include Lil's Loose Tooth, Richard Scarry's Best Word Book Ever, and Winnie the Pooh in A Sweet Good Morning. The set also includes a paper piano keyboard and map and human anatomy games. Gail Hudson Batteries: 4 AA batteries required. Barron's Math Workbook for the Sat I (Barron's Math Workbook for the Sat I, 2nd Ed) Visit Our Sites: Buy Law Books Top Quality Wrist Watches

64. Sketches Of An Elephant: A Topos Theory Compendium (Oxford Logic Guides, 43 & 44 Book Stores Book Reviews Sketches of an Elephant A topos theoryCompendium (Oxford Logic Guides, 43 44). Sketches of an Elephant http://www.bookfinder.us/review9/019852496X.html

Elephants Book Review AUTHOR: Peter T. Johnstone ISBN: 019852496X Compare price for this book Children's Book Animals Elephants - Book Review, by Peter T. Johnstone From the Publisher Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Now available in this two volume set, it contains all the important information both volumes provides. Considered to be a complete benefit for all researchers and academics in theoretical computer science, logicians and philosophers who study the foundations of mathematics, and those working in differential geometry and continuum physics. Compare prices for this book Children's Book Animals Elephants

65. Toward A New Understanding Of Space, Time And Matter: Workshops Chris Isham. Thursday, June 17, 330 pm 530 pm, Category theory,topos theory, and topological quantum field theory, Lou Kauffman. http://axion.physics.ubc.ca/Workshop/Workshops.html

Toward a New Understanding of Space, Time, and Matter Workshop Schedule June 16-19, 1999 All workshops take place in the large Peter Wall Institute conference room on the third floor of the University Centre Wednesday, June 16 7:30 pm - 9:30 pm Post-talk discussion Steve Weinstein Thursday, June 17 9:30 am - 11:30 am What is a quantum theory? Chris Isham Thursday, June 17 3:30 pm - 5:30 pm Category theory, topos theory, and topological quantum field theory Lou Kauffman Thursday, June 17 7:30 pm - 9:30 pm Spacetime in string/M-theory Tamiaki Yoneya Friday, June 18 9:30 am - 11:30 am Time and space in physical theory and experience Larry Sklar Friday, June 18 3:30 pm - 5:30 pm Field-theoretic issues in quantum gravity Lee Smolin Saturday, June 19 9:30 am - 11:30 am Quantum gravity: physics, metaphysics, or mathematics? Simon Saunders Saturday, June 19

66. Casual Category Theory - Fall 2000 Tuesday 1215 24/10/2000 (Luigi Santocanale), Introduction to topos theoryI ll define elementary toposes and introduce their basic properties. http://www.brics.dk/~varacca/CCT/cct-fall00.html

Casual Category Theory - Fall 2000 Events in time-directed order Tuesday 12:15 (Luigi Santocanale) Introduction to topos theory [MM] (Other possible references: McLarty [CML] [BW] Tuesday 12:15 (Luigi Santocanale) Introduction to topos theory (continuation) Some properties of elementary toposes. The subobject classifier in a presheaf topos. Beck's theorem. Tuesday 9:15 (Pawel Sobocinski) Introduction to topos theory (continuation) Tutorial: proving properties in toposes. An alternative definition of topos. Tuesday 12:15 (Luigi Santocanale) Categorical logic. The internal language of a topos. [LS] Tuesday 12:15 (Luigi Santocanale) The internal language of a topos (continuation). The Kripke-Joyal semantics. Tuesday 12:15 (Daniele Varacca) Tutorial: using categorical logic. The Heyting algebra of subobjects. The extension of a formula of the internal language. Tuesday 12:15 (Daniele Varacca) Tutorial: using categorical logic II.

67. FIRST Graduate School: Seminars topos theory Study Group Goal of this seminar is to study aspects oftopos theory relevant to computer science. After reading sections http://first.dk/activities/seminars.html

FIRST Graduate School: Seminars (Activities) The are a number of seminars and study groups relevant to members of the PhD school. Seminars Please check the homepages of the seminars for up-coming events. Algorithmics and Optimization Research talks are presented in the area of algorithms and optimization. Time: Friday, 13:15 - 14:00 Place: N037 (DIKU) Contact: David Pisinger COPLAS CO penhagen P rogramming LA nguage S eminar: The programming language groups at the Department of Computer Science, University of Copenhagen (DIKU), at The IT University of Copenhagen (IT-C) and at the Royal Veterenary and Agricultural University (KVL) organize a joint series of weekly seminars in programming languages: the Copenhagen Programming Language Seminar. Its purpose is to exploit the proximity of the institutions to strengthen the integration between the programming language groups in the Copenhagen area and to present state-of-the-art research to students, academics and industry. Time: Thursday, 15:15 - 16:00

68. Prof. P.T. Johnstone Research Interests I have been involved in the development of elemntary topos theorysince its infancy in the early 1970s, and have written two books on the http://www.dpmms.cam.ac.uk/site2002/People/johnstone_pt.html

Department of Pure Mathematics and Mathematical Statistics DPMMS People Prof. P.T. Johnstone Prof. P.T. Johnstone Title: Professor of the Foundations of Mathematics College: St John's College Room: C1.07 Tel: +44 1223 337985 Research Interests: I have been involved in the development of elemntary topos theory since its infancy in the early 1970s, and have written two books on the subject: "Topos Theory" (Academic Press, 1977) and "Sketches of an Elephant: a Topos Theory Compendium" (Oxford U.P., 2002). My interests focus particularly on the way in which topos theory provides a means of integrating geometric and logical ideas in the foundations of mathematics and of theoretical computer science. Information provided by webmaster@dpmms.cam.ac.uk

69. Siberian Toposes Below we gave the papers in which applications of topos theory to the modern TheoreticalPhysics are discussed discussed. AXIOMATIC THEORY OF RELATIVITY. http://users.univer.omsk.su/~topoi/appl_e.html

Below we gave the papers in which applications of topos theory to the modern Theoretical Physics are discussed discussed. AXIOMATIC THEORY OF RELATIVITY Guts, A.K. A topos-theoretic approach to the foundations of Relativity theory Soviet Math. Dokl.- 1991.-V.43, No.3.-P.904-907. GENERAL THEORY OF RELATIVITY and THEORY OF GRAVITY Trifonov, V. Linear Solution of the Four-Dimensionality Problem Europhys. Lett. 1995. V.32, N.8, P.621-626. Grinkevich, E.B. Synthetic Differential Geometry: A Way to Intuitionistic Models of General Relativity in Toposes Preprint gr-qc/9608013 Guts, A.K., Grinkevich, E.B. Toposes in General Theory of Relativity. Preprint gr-qc/9610073 Guts, A.K. Intuitionistic Theory of Space-time (russian) // Zvyagintsev, A.A. Pseudo-Euclidean space in model of Synthetic Differential Geometry (russian) // Mathematical Structures and Modeling. 1998. No. 2. P.34-38. Guts, A.K., Zvyagintsev, A.A. Solution of the vacuum Einstein equations in Synthetic Differential Geometry of Kock-Lawvere . - Paper: physics/9909016. Guts, A.K., Zvyagintsev, A.A.

70. News Letter Vol.5 No.3 a more general interpretation of fuzzy logic within the environment of other propercategories of fuzzy sets stemming either from the topos theory, or even http://www.erudit.de/erudit/newsletters/news_53/page10.htm

New Books / Journals MATHEMATICAL PRINCIPLES OF FUZZY LOGIC Vilem Novak, Irina Perfilieva, Jiri Mockor Kluwer Academic Publishers, Boston/DordrechtLondon 1999. ISBN 0-7923-8595-0 MATHEMATICAL PRINCIPLES OF FUZZY LOGIC provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what, and how it can be represented by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of the common-sense human reasoning, which is based on the use of natural language, the distinguishing feature is vagueness of its semantics. MATHEMATICAL PRINCIPLES OF FUZZY LOGIC will be of interest to all researchers of fuzzy logic, including mathematicians and computer scientists interested in the mathematical aspects of fuzzy logic. It may be used as a text in advanced level courses on various fuzzy logic applications, artificial and computational intelligence, decision-making and more.

71. Subject Classification topos theory. 11. Comments on the Development of topos theory, Development of Mathematics19502000, Ed. by JP Pier, Birkhauser Verlag, Basel, 2000. Philosophy. http://www.acsu.buffalo.edu/~wlawvere/subject.html

F. William Lawvere Subject Classification of Articles HOME Chronological list Functorial Semantics of Algebraic Theories Proceedings of the National Academy of Science 50 , No. 5 (November 1963), 869-872. Algebraic Theories, Algebraic Categories, and Algebraic Functors, Theory of Models ; North-Holland, Amsterdam (1965), 413-418. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories Springer Lecture Notes in Mathematics No. 61 , Springer-Verlag (1968), 41-61. Review of P. M. Cohn's Universal Algebra , 2nd Edition, American Scientist (May-June 1982), p. 329. 42. with J. Adamek and J. Rosicky, How algebraic is algebra? Theory and Applications of Categories (2001) 253-283 (electronic). 44. with J. Adamek and J. Rosicky: On the duality between varieties and algebraic theories, Algebra Universalis, Topos Theory Quantifiers and Sheaves Proceedings of the International Congress on Mathematics , (Nice 1970), Gauthier-Villars (1971) 329-334. Introduction to the Proceedings of the Halifax Conference, Toposes, Algebraic Geometry and Logic Springer Lecture Notes in Mathematics No. 274

72. MainFrameDefinitions Of Pure Categories And Functors. vocabulary. Perhaps the most common approach to categorical foundationsfollows this line, usually through topos theory. The idea http://www.rbjones.com/rbjpub/pp/gst/pcf-defns-m.html

73. Marta Bunge Title of invited talk Galois groupoids and covering morphisms in topos theory http//www.fields.utoronto.ca/programs/scientific/0203/galois_and_hopf/ 2003. http://www.math.mcgill.ca/bunge/meetings.html

Meetings CMS Summer Meeting 2002. Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories. (Org.: George Janelidze, Bodo Pareigis and Walter Tholen) The Fields Institute for Research in the Mathematical Sciences, University of Toronto, September 23-28, 2000. Visiting Academic. Title of invited talk: "Galois groupoids and covering morphisms in topos theory" http://www.fields.utoronto.ca/programs/scientific/02-03/galois_and_hopf/ Union College Mathematics Conference (with concurrent sessions in Algebraic Topology, Category Theory, and Differential Geometry) (Org. Category Theory: Susan Niefield and Kimmo Rosenthal) Union College. Department of Mathematics. Schenectady, NY. November 8-9, 2003. Title of talk : "Groupoids, locally paths connected toposes, and a Van Kampen theorem " http://www.math.union.edu/~leshk/03Conference/ Workshop on the Ramifications of Category Theory (including a featured series of lectures by F.W. Lawvere) (Org.: Alberto Peruzzi and Michael Wright) University of Florence, Florence, Italy, November 18-22. Title of invited talk: " Totally disconnected reflections in the homotopy theory of toposes ". http://ramcat.scform.unifi.it CMS Summer Meeting 2004.

74. CATEGORY THEORY AT MCGILL Differential Algebra, Homological Algebra, Synthetic Differential Geometry andTopology, Hopf Algebras and Dynamical Systems, topos theory, Locales Theory http://www.math.mcgill.ca/bunge/ctatmcgill.html

Category Theory at McGill Silvia Bunge and Carl Christian Mikkelsen, Montreal '78 Category Theory Category theorists are conceptual mathematicians of a special kind. What binds them together is that they approach mathematical problems with a point of view that is radically different from that on which traditional mathematics is based, and which emphasizes interactions between mathematical objects over their individual constituents. Their results are often surprising, provide new insights, and are obtained by the invention of sophisticated notions, theories, and techniques. Category Theory is only little more than 50 years old (dating it back to the work of S. Eilenberg and S. MacLane in 1945) yet, its impact on several branches of mathematics has been considerable, in spite of the reluctance to recognize it as a revolutionary independent field dealing with foundational questions, very different from Set Theory. Category Theory at McGill The Montreal Categories Center Current Research Areas in Category Theory at McGill Three areas deserve attention because of the novelties they bring and because they are part of a truly international joint effort. Let us refer to them as "Grothendieck's Program", "Lawvere's Program", and "Computational Category Theory". Although not pairwise disjoint, their objectives are different and can be briefly described as follows.

75. Syllabus Query -- 2004/2005 S. Mac Lane and Ieke Moerdijk. Sheaves in Geometry and Logic A FirstIntroduction to topos theory, Springer, 1992. PT Johnstone. http://mma.math.ist.utl.pt/prog.phtml.en?disc=TeCa&sem=1

76. SUO: Re: IFF Comments Requested however. These are distinctions in the foundations of topos theory,not the usual fodder of the working mathematician. PH Most http://suo.ieee.org/email/msg06683.html

Thread Links Date Links Thread Prev Thread Next Thread Index Date Prev ... Date Index SUO: Re: IFF Comments Requested To jawbrey@oakland.edu Subject : SUO: Re: IFF Comments Requested From phayes@ai.uwf.edu Date : Mon, 8 Oct 2001 15:36:21 -0500 Cc standard-upper-ontology@ieee.org In-Reply-To 3BC20300.3F9ADAF0@oakland.edu References 3BBCF80F.15BC2FE2@oakland.edu 3BC20300.3F9ADAF0@oakland.edu Reply-To phayes@ai.uwf.edu Sender owner-standard-upper-ontology@majordomo.ieee.org http://www.coginst.uwf.edu/~phayes Follow-Ups SUO: Re: IFF Comments Requested From: References SUO: Re: IFF Comments Requested From: SUO: Re: IFF Comments Requested From: SUO: Re: IFF Comments Requested From: SUO: Re: IFF Comments Requested From: Prev by Date: Re: [Fwd: [Fwd: SUO: John Sowa's motion]] Next by Date: SUO: Modularity (and conformance) Prev by thread: SUO: Re: IFF Comments Requested Next by thread: SUO: Re: IFF Comments Requested Index(es): Date Thread

77. Re: SUO: Re: IFF Comments Requested Are you meaning to suggest that topos theory is likely to provide a goodfoundation for a psychological theory of performance of novices? http://suo.ieee.org/email/msg06674.html

Thread Links Date Links Thread Prev Thread Next Thread Index Date Prev ... Date Index Re: SUO: Re: IFF Comments Requested To josiane.caron@mshs.univ-poitiers.fr Subject : Re: SUO: Re: IFF Comments Requested From phayes@ai.uwf.edu Date : Mon, 8 Oct 2001 13:40:09 -0500 Cc standard-upper-ontology@ieee.org In-Reply-To 4.2.0.58.20011006103931.009f48a0@pop.mshs.univ-poitiers.fr References 4.2.0.58.20011006103931.009f48a0@pop.mshs.univ-poitiers.fr Reply-To phayes@ai.uwf.edu Sender owner-standard-upper-ontology@majordomo.ieee.org http://www.coginst.uwf.edu/~phayes References Re: SUO: Re: IFF Comments Requested From: Prev by Date: Re: SUO: Re: IFF Comments Requested Next by Date: SUO: Re: IFF Comments Requested Prev by thread: Re: SUO: Re: IFF Comments Requested Next by thread: Re: SUO: Re: IFF Comments Requested Index(es): Date Thread

78. Topos, Foliations And All That By Alejandro Rivero Second, I want to ask if some Topos/Sheaf fanatic have studied relationship betweenthe generalized spaces etc of topos theory, and the nonconmutative spaces http://mathforum.org/epigone/sci.math.research/smerdwhilple/1993Jan22.210826.123

Topos, Foliations and all that by Alejandro Rivero reply to this message post a message on a new topic Back to sci.math.research Subject: Topos, Foliations and all that Author: rivero@sol.cie.unizar.es Organization: Department of Theoretical Physics. University of Zaragoza Date: Fri, 22 Jan 1993 21:08:26 GMT First of all, let me to add to the bibliography a nice book we have just got: Sheaves in Geometry and Logic, By S MacLane and Ieke Moerdijk, Springer. Second, I want to ask if some Topos/Sheaf fanatic have studied relationship between the generalized spaces etc of Topos theory, and the non-conmutative "spaces" of Alain Connes. Im not expert in the matter, so I could be asking a nonsense. Anyway, a motivation for the question is that the Kroneker foliation of the bidimensional torus, which were the main example of Connes' theory, is also one principal example of Sheaf/Topos theory when used to calculate De Rham Homology. At least, it is used by Moerdijk (althought not in that book) to show all the constructios of clasifiyng topos, BG etc... -Alejandro Rivero Zaragoza Univ, Spain rivero@cc.unizar.es or rivero@sol.cie.unizar.es The Math Forum

79. Philosophia Mathematica Abstracts: Vol. 11 Category theory and topos theory have been seen (by Mac Lane, Bell, Awodey, et al.)as providing a structuralist framework for mathematics autonomous vis à http://www.umanitoba.ca/pm/absvol11.html

ABSTRACTS OF PAPERS IN VOLUME ELEVEN TABLE OF CONTENTS Jeremy Avigad, Number theory and elementary arithmetic Helen Billinge, Did Bishop Have a Philosophy of Mathematics? Roy T. Cook, Aristotelian Logic, Axioms, and Abstraction Elizabeth F. Cooke, Peirce, Fallibilism, and the Science of Mathematics E. B. Davies, Empiricism in arithmetic and analysis Geoffrey Hellman, Does Category Theory Provide a Framework for Mathematical Structuralism? David Liggins, On Being Twice as Heavy A Second Glance at Non-restrictiveness Graham Priest, Meinongianism and the Philosophy of Mathematics Success by Default? Greg Restall, Just What Is Full-Blooded Platonism? Peter Roeper, Giving an Account of Provability Within a Theory William Stirton, Caesar Invictus Gabriel Uzquiano, Plural Quantification and Classes Papers accepted are listed under Abstracts Updated 2003 8 17 Back to the Philosophia Mathematica main page. JEREMY AVIGAD, avigad@cmu.edu Number theory and elementary arithmetic ABSTRACT. Elementary arithmetic (also known as ``elementary function arithmetic'') is a fragment of first-order arithmetic so weak that it cannot prove the totality of an iterated exponential function. Surprisingly, however, the theory is remarkably robust. I will discuss formal results that show that many theorems of number theory and combinatorics are derivable in elementary arithmetic, and try to place these results in a broader philosophical context. HELEN BILLINGE, h.billinge@lse.ac.uk

80. Abstracts The general mathematician, who regards category theory as `generalized abstractnonsense, tends to regard topos theory as generalized abstract category theory http://math.arizona.edu/~gradcolloq/fll01abs.html

August 29 Speaker - Alan Von Hermann Title - Von Neumann Regular Rings In this talk, I will give some classical examples of Von Neumann Regular Rings (VNRR) and discuss some interesting properties that such rings have. In particular, I will give a sufficient condition for a VNRR to be a division ring. Undergraduates with some background in Algebra are encouraged to attend. September 5 Speaker - Katrina Jimenez,Jennifer Christian Smith, and William Y. Velez Title - Outreach Opportunities for Graduate Students Outreach activities are a fun, rewarding way to add some spark to your resume during graduate school. We will present a variety of ways that you can get involved in outreach activities with local high school students through a developing program coordinated by graduate students in the department. Two types of outreach activities, the development and presentation of weekday mathematics workshops for high school students and "special guest" visits to local calculus classes, will be discussed. Students with VIGRE support are especially encouraged to get involved this year. Come and learn how you can get involved! September 12 Speaker - David Gay Title - How to Draw Pictures of 4-Manifolds This is partly designed as an introduction to some upcoming talks I will give in the geometry seminar, but it should also be entertaining all by itself. I will discuss "Kirby calculus", a technique for drawing pictures of 4-manifolds using knots and links; this is old-fashioned topology (no PDE's, no moduli spaces, no connections on weird bundles) but it continues to be a useful tool in modern work on 4-manifolds. I will also talk about how to add a little extra structure and use Kirby calculus to think about symplectic 4-manifolds.

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