21. School Of Computer Science - Dr Steve Vickers University of Birmingham, UK - Geometric logic, topos theory, quantales and semantics of programming languages. http://www.cs.bham.ac.uk/~sjv/

Search School of Computer Science Personal Web Page Skip past menu to page content Home ~sjv Skip past menu to page content ... Home Steve Vickers Skip past menu to page content Steve Vickers's home page Research Papers ... Turtle Graphics Dr Steve Vickers School of Computer Science The University of Birmingham Birmingham, B15 2TT, UK. email: s.j.vickers 'at' cs.bham.ac.uk Tel: 0121-414 3743 NEWS! Midland Graduate School In the 2010 Midland Graduate School in the Foundations of Computer Science I am teaching an advanced course on Quantum Topos Theory NEWS! New research project started September 2009 EPSRC has announced funding for my proposal for a project Applications of geometric logic to topos approaches to quantum theory , an interdisciplinary project to apply my mathematical research to some new applications of topos theory to physics. Research My particular research interests are in geometric logic, topology and topos theory. These are areas of mathematics that have connections with computer science, although my work in them is often purely mathematical. A particular focus at present, funded by an EPSRC grant, is the connections with some new topos approaches to quantum physics. On the research page you can also find opportunities for PhD study with me.

22. CiteULike: Sheaves In Geometry And Logic: A First Introduction To Topos Theory ( by S MacLane Cited by 1030 - Related articles http://www.citeulike.org/user/hhalvors/article/423554

Search all the public and authenticated articles in CiteULike. Enter a search phrase. You can also specify a CiteULike article id ( a DOI ( doi:10.1234/12345678 or a PubMed Id ( pmid:12345678 Click Help for advanced usage. CiteULike hhalvors's CiteULike Search Register Log in Home ... Research Fields NEW Help/FAQ Discussion Contact Us Library ... Recommendations NEW Neighbours Watchlist CiteULike is a free online bibliography manager. Register and you can start organising your references online. Tags Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext) by: Saunders MacLane Ieke Moerdijk RIS Export as RIS which can be imported into most citation managers BibTeX Export as BibTeX which can be imported into most citation/bibliography managers PDF Export formatted citations as PDF RTF Export formatted citations as RTF which can be imported into most word processors Delicious Export in format suitable for direct import into delicious.com. Setup a permanent sync to delicious) Formatted Text Export formatted citations as plain text To insert individual citation into a bibliography in a word-processor, select your preferred citation style below and drag-and-drop it into the document.

23. Topos Theory As A Framework For Partial Truth - PhilSci-Archive This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum http://philsci-archive.pitt.edu/archive/00000192/

@import url(/style/auto.css); @import url(/style/print.css); @import url(/style/nojs.css); Login Create Account Simple Search Advanced Search ... Latest Additions Information Home About the Archive Archive Policy History ... Contact Us Topos Theory as a Framework for Partial Truth Butterfield, Jeremy Topos Theory as a Framework for Partial Truth. [Preprint] Preview PDF Download (221Kb) Preview Preview Postscript Download (266Kb) Preview Abstract Export/Citation: EndNote BibTeX Dublin Core ASCII (Chicago style) ... OpenURL Social Networking: Share Item Type: Preprint Keywords: Topos theory, category theory, partial truth, Kochen-Specker theorem, intuitionistic logic Subjects: Depositing User: Jeremy Butterfield Date Deposited: 09 Mar 2001 Last Modified: 07 Oct 2010 11:10 Item ID: URI: http://philsci-archive.pitt.edu/id/eprint/192 Actions (login required) View Item ULS D-Scribe This site is hosted by the University Library System of the University of Pittsburgh as part of its D-Scribe Digital Publishing Program E-Prints Philsci Archive is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton.

24. Topos Theory wordtrade.com reviews in mathematical topics Mathematics Review Essays of Academic, Professional Technical Books in the Humanities Sciences http://www.wordtrade.com/science/mathematics/topostheory.htm

Wordtrade.com Mathematics WT Main About WT Review Links Contact ... Sketches of an Elephant : A Topos Theory Compendium by Peter T. Johnstone Oxford Oxford University Press) Topos theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject. Topos: A category modeled after the properties of the category of sets. 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. Citing the old Indian story about the blind men feeling different parts of an elephant and coming up with divergent descriptions of the animal Johnstone says that topos theory can be described in divergent ways depending on what part is examined. The original conception of toposes arose in the 1960s as a "generalized space" supporting cohomology theory, but has grown to be used by category theory and other branches of mathematics. Addressing those already familiar with topos theory, Johnstone offers these volumes (and a scheduled 3rd) as a complete treatment of all of the pieces of elementary topos theory together with fully worked-out results. Volume one discusses toposes as categories. Toposes as spaces and theories are reserved for the second. The final volume expected to discuss homotopy and cohomology, and toposes as mathematical universes.

25. OUP: Johnstone: Sketches Of An Elephant: A Topos Theory Compendium: - Oxford Uni 2 Volume Set This item is printed to order and supplied on a firm sale basis. Items which are printed to order are normally despatched and charged within 510 days. http://ukcatalogue.oup.com/product/9780198524960.do

26. Re: [Axiom-developer] Unions In Spad We know from very general considerations (topos theory) that if we expect to be able to implement a large part of mathematics (e.g.that part http://www.mail-archive.com/axiom-developer@nongnu.org/msg11353.html

axiom-developer Thread Date Re: [Axiom-developer] Unions in Spad Bill Page Thu, 12 Jul 2007 23:16:32 -0700 .. Whatever the primitive types are, the important thing is that there be a well-designed user interface (exported functions) on par with all other algebra code. Right now, Tuple and Union are "inaccessible" from the algebra layer without going to lisp (Record seems okay ). That is, in my view, a design flaw. They should be designed as if they were genuine domains (where one can construct elements and extract information from elements and compute with them). How they are implemented and optimized at the lower levels should not be of concern to the algebra layer. http://www.math.ucr.edu/home/baez/topos.html http://en.wikipedia.org/wiki/Image_ (mathematics) This bias against these dual notions runs very deep and effects the expressiveness of our mathematical programming language in important concepts such as equivalence classes and equality as well as many fundamental ideas that arise in algebraic topology. Which again emphasizes the role of category theory and the need to "get it right" in the choice of primitive types. Further ref: http://en.wikipedia.org/wiki/Topos_theory

27. Topos Theory Category Mathematics Sets Introduction Cambridge Topos Theory Category Mathematics Sets Introduction Cambridge Economy. http://www.economicexpert.com/a/Topos.htm

28. Sheaf And Topos Theory In NLab Idea. Topos theory is the part of category theory that studies categories which are topos es. This includes in particular Grothendieck topos es, i.e. categories of sheaves. http://ncatlab.org/nlab/show/sheaf and topos theory

nLab sheaf and topos theory Skip the Navigation Links Home Page All Pages Recently Revised ... Export Context Topos Theory topos theory Toposes Background category theory category functor Toposes (0,1)-topos Heyting algebra locale pretopos ... quasitopos Internal Logic internal logic type theory subobject classifier natural numbers object Topos morphisms geometric morphism direct image inverse image global sections ... logical morphism Extra stuff, structure, properties topological locale localic topos petit topos/gros topos locally connected topos ... smooth topos Cohomology and homotopy cohomology homotopy abelian sheaf cohomology model structure on simplicial presheaves In higher category theory higher topos theory (0,1)-topos (0,1)-site 2-topos ... Edit this sidebar Category Theory category theory Concepts category functor natural transformation Cat Universal constructions universal construction representable functor adjoint functor limit ... Kan extension Theorems Yoneda lemma Isbell duality Grothendieck construction adjoint functor theorem ... Tannaka duality Extensions sheaf and topos theory enriched category theory higher category theory Applications applications of (higher) category theory Edit this sidebar topos theory 2-topos theory (∞,1)-topos theory

29. Topos In NLab Ross Street, A survey of topos theory (notes for students, 1978) pdf; A standard textbook is. Peter Johnstone, Topos theory, London Math. Soc. Monographs 10, Acad. Press 1977, xxiii+367 http://ncatlab.org/nlab/show/topos

nLab topos Skip the Navigation Links Home Page All Pages Recently Revised ... Export Context Topos Theory topos theory Toposes Background category theory category functor Toposes (0,1)-topos Heyting algebra locale pretopos ... quasitopos Internal Logic internal logic type theory subobject classifier natural numbers object Topos morphisms geometric morphism direct image inverse image global sections ... logical morphism Extra stuff, structure, properties topological locale localic topos petit topos/gros topos locally connected topos ... smooth topos Cohomology and homotopy cohomology homotopy abelian sheaf cohomology model structure on simplicial presheaves In higher category theory higher topos theory (0,1)-topos (0,1)-site 2-topos ... Edit this sidebar Category Theory category theory Concepts category functor natural transformation Cat Universal constructions universal construction representable functor adjoint functor limit ... Kan extension Theorems Yoneda lemma Isbell duality Grothendieck construction adjoint functor theorem ... Tannaka duality Extensions sheaf and topos theory enriched category theory higher category theory Applications applications of (higher) category theory Edit this sidebar Contents Idea Definition Properties Reasoning in a topos ... References Idea There are many different perspectives on the notion of topos . One useful one is that a topos is a category that looks like a category of space s that sit by local homeomorphism s over a given base space : all spaces that are locally modeled on a given base space.

30. Topoi For Physics Valuations In The Language Of Topos Theory “Useful as it is under everyday circumstances to say that the world exists “out there” independent of us, that view can no longer be upheld. http://topos-physics.org/topos-and-logic

Where Geometry meets Dynamics Topoi for Physics Valuations in the language of Topos theory Wheeler (1983) . Precisely: propositions in Classical Physics form a Boolean algebra, while propositions in Quantum Mechanics form a non-Boolean algebra. An attempt to give Quantum Mechanics the status of a realist theory is given by the hidden variable theories, which postulate the following: in any state values of observables A are determined by and hidden variables. However these theories where disproved by the Kochen-Specker Theorem and Bell inequalities , both of which show that properties are not possessed by a Quantum System, therefore rejecting the first assumption of the Hidden variable theories. In particular, the Kochen-Specker theorem asserts that it is impossible to evaluate propositions regarding values possessed by physical entities represented by projection operators, such that their truth values belong to the set therefore depriving of meaning any statement regarding a state of affairs of a system, since, generally speaking, a statement is said to be meaningful if its validity can be assessed. The Bell inequalities go further and show the impossibility of a local realist interpretation of Quantum Mechanics.

31. A Few Points In Topos Theory - Microsoft Academic Search Authors Sam Zoghaib. Citations 0 This paper deals with two problems in topos theory; the construction of finite pseudolimits and pseudo-colimits in appropriate sub-2-categories http://academic.research.microsoft.com/Paper/5633080.aspx

var SiteRoot = 'http://academic.research.microsoft.com'; SHARE Author Conference Journal Year Look for results that meet for the following criteria: since equal to before Publication A few points in topos theory Edit A few points in topos theory Sam Zoghaib This paper deals with two problems in topos theory; the construction of finite pseudo-limits and pseudo-colimits in appropriate sub-2-categories of the 2-category of toposes, and the definition and construction of the fundamental groupoid of a topos, in the context of the Galois theory of coverings; we will take results on the fundamental group of étale coverings in (1) as a starting example for the latter. We work in the more general context of bounded toposes over Set (instead of starting with an eec- tive descent morphism of schemes). Questions regarding the existence of limits and colimits of diagram of toposes arise while studying this prob- lem, but their general relevance makes it worth to study them separately. We expose mainly known constructions, but give some new insight on the assumptions and work out an explicit description of a functor in a coequalizer diagram which was as far as the author is aware unknown, which we believe can be generalised. This is essentially an overview of study and research conducted at dpmms, University of Cambridge, Great Britain, between March and Au- gust 2006, under the supervision of Martin Hyland. View or Download

32. Gonzalo E. Reyes - Marie La Palme Reyes · Topos Theory From mathematics to literature. Des math matiques la litt rature. You are currently browsing the archive for the Topos theory category. http://po-start.com/reyes/category/topos-theory/

Gonzalo E. Reyes - Marie La Palme Reyes From mathematics to literature. - Des mathématiques à la littérature. Home Coups de coeur / Favorites Marie La Palme Reyes Gonzalo E. Reyes ... Subscribe to feed Topos theory You are currently browsing the archive for the Topos theory category. Generic figures and their glueings, A constructive approach to functor categories 1 June, 2004 in Book Categorical logic Gonzalo E. Reyes Marie La Palme Reyes ... Works on line by marie Generic figures and their glueings, A constructive approach to functor categories. Polimetrica, corso Milano 26, Monza (MI). Marie La Palme Reyes, Gonzalo E. Reyes and Houman Zolfaghari Abstract samplebook.pdf Strong amalgamation, Beck-Chevalley for equivalence relations and interpolation in Algebraic Logic 1 June, 2003 in Article Categorical logic Gonzalo E. Reyes Mathematics ... Works on line by gonzalo Galli, A., Reyes G.E. and M. Sagastume (2003). Strong amalgamation, Beck-Chevalley for equivalence relations and interpolation in Algebraic Logic. Fuzzy sets and systems 138, 3-23. Strong Amalgamation Completeness theorems via the double dual functor 1 June, 2000 in

33. Topos Theory - File Search (5927 Results) Download topos theory from Rapiddigger.com. Files PA Topos NadaQueHacer .rar, topos cfos full .rar http://rapiddigger.com/topos-theory/

var content_type = "all"; General search Video search Results for topos theory from File search Like this Friend us Tweet this Follow us ... Ap 1977 .djvu Source: sponsored link Johnstone Topos Theory Ap 1977 .djvu Source: http://www.ufindbook.com/index/page-25064.html johnstone topos theory ap 1977 .djvu Rapidshare Type: djvu Mirrors: Parts: 1 parts Total size: 23,442 KB Number theory .rar Source: http://www.taringa.net/posts/ebooks-tutoriales/1543090/%5BMegapost%5D-Ebooks-matem%C3%A1ticas-(Ingl%C3%A9s)-Muy-bueno!.html number theory .rar Rapidshare Type: rar Mirrors: Parts: 7 parts Total size: 439,863 KB Hybrid Theory .zip Source: http://vb.lll1.com/%D8%A7%D8%BA%D8%A7%D9%86%D9%8A-%D8%B1%D9%88%D9%83-%D9%85%D8%AA%D9%84-%D9%87%D8%A7%D8%B1%D8%AF-%D8%B1%D9%88%D9%83-139/%D8%AC%D9%85%D9%8A%D8%B9-%D8%A7%D9%84%D8%A8%D9%88%D9%85%D8%A7%D8%AA-%D9%81%D8%B1%D9%82%D8%A9-linkin-park-10478.html hybrid theory .zip Rapidshare Type: zip Mirrors: Parts: 3 parts Total size: 215,961 KB Wave Theory .PDF Source: http://forexone.wordpress.com/download-area wave theory .pdf

34. CiteSeerX — On Branched Covers In Topos Theory CiteSeerX Document Details (Isaac Councill, Lee Giles) We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.1596

35. CiteULike: Tag Topos-theory [103 Articles] Perspectives of Systems Informatics 5th International Andrei Ershov Memorial Conference, PSI 2003, Akademgorodok, Novosibirsk, Russia, July 912, 2003, http://www.citeulike.org/tag/topos-theory

36. Topos Theory Facts - Freebase Facts and figures about Topos theory, taken from Freebase, the world's database. http://www.freebase.com/view/en/topos

37. Topos Theory And Constructive Logic Papers Of Andreas R. Blass Topos Theory and Constructive Logic Papers Andreas Blass . Papers on linear logic are on a separate page. http://www.math.lsa.umich.edu/~ablass/cat.html

Topos Theory and Constructive Logic Papers Andreas Blass Papers on linear logic are on a separate page The interaction between category theory and set theory (in "Mathematical Applications of Category Theory," edited by J. Gray, Contemporary Mathematics 30 (1984) 529) PDF This paper is based on a lecture about the various connections between category theory and set theory. Some interactions arise from set theory's foundational role in mathematics. Others arise from category theory's role of clarifying and unifying concepts in many areas of mathematics. We also discuss categories with set-theoretic structure, primarily topoi, and some suggestive but not fully understood connections between particular topics in set theory and category theory. I thank Dave Childs for producing an electronic version of this paper. An induction principle and pigeonhole principle for K-finite sets (J. Symbolic Logic 59 (1995) 11861193) PostScript or PDF We establish a course-of-values induction principle for K-finite sets in intuitionistic type theory. Using this principle, we prove a pigeonhole principle conjectured by Benabou and Loiseau. We also comment on some variants of this pigeonhole principle. Seven trees in one (J. Pure Appl. Alg. 103 (1995) 1-21)

38. Topos Theory Seminar --- Fall 2004 This is a Ph.D. seminar in which we study aspects of topos theory relevant to computer science. After having read material from Peter Johnstone's opus Sketches of an Elephant http://www.itu.dk/people/birkedal/teaching/topos-theory-Fall-2004/

Topos Theory Seminar Fall 2004 Organizers: Lars Birkedal birkedal@itu.dk , Room 4C 15, 7218 5280 Carsten Butz butz@itu.dk , Room 4C 14, 7218 5274 This is a Ph.D. seminar in which we study aspects of topos theory relevant to computer science. After having read material from Peter Johnstone's opus Sketches of an Elephant: A Topos Theory Compendium , Lambek/Scott's Introduction to higher order categorical logic , Mac Lane/Moerdijk's Sheaves in Geometry and Logic we plan to continue with a semester on realizability toposes (without assuming too much knowledge of the material covered in previous semesters to allow new students to participate). Additional material can be found at Jaap van Oosten's page with links to recent articles on realizability and at Lars Birkedal's (somewhat dated) online bibliography on realizability The main goal of the seminar this Fall is to get an understanding of various realizability toposes and how theses are constructed from so-called triposes. In particular, we'll address recent attempts to create realizability toposes for Godel's dialectica interpretation. Further off-line topics could include how realizability toposes may be constructed and analyzed using exact completions; a deeper analysis of subcategories of realizablity toposes; how one may understand Krivine's notion of realizabilty as a tripos / topos; application of realizability models in semantics of programming languages; etc.

39. [0803.0417] `What Is A Thing?': Topos Theory In The Foundations Of Physics Abstract The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire http://arxiv.org/abs/0803.0417

arXiv.org quant-ph Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: quant-ph new recent Change to browse by: gr-qc hep-th math math-ph ... what is this? Bookmark what is this? Quantum Physics Title: Authors: Andreas Doering Chris Isham (Submitted on 4 Mar 2008) Abstract: The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. In doing so we provide a new answer to Heidegger's timeless question ``What is a thing?''. Comments: To appear in ``New Structures in Physics'' ed R. Coecke Subjects: Quantum Physics (quant-ph) ; General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:0803.0417v1 [quant-ph] Submission history From: Chris Isham [ view email Tue, 4 Mar 2008 11:38:15 GMT (167kb)

40. Www.math.niu.edu From baez@galaxy.ucr.edu (John Baez) Subject Topos theory for physicists. Date 28 Dec 2000 191247 GMT. Newsgroups sci.physics.research. Summary missing http://www.math.niu.edu/~rusin/known-math/00_incoming/topos

From: baez@galaxy.ucr.edu (John Baez) Subject: Topos theory for physicists Date: 28 Dec 2000 19:12:47 GMT Newsgroups: sci.physics.research Summary: [missing] In article

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