41. Categories: Topos Theory And Large Cardinals Andrej Bauer asked whether large cardinals other than inaccessible ones have a natural definition in topos theory. Indeed, like most questions of set theory which have an http://north.ecc.edu/alsani/ct99-00(8-12)/msg00128.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Topos theory and large cardinals To categories@mta.ca Subject : categories: Topos theory and large cardinals From wlawvere@acsu.buffalo.edu Date : Tue, 21 Mar 2000 16:32:09 -0500 (EST) Reply-To wlawvere@acsu.buffalo.edu Sender cat-dist@mta.ca http://www.acsu.buffalo.edu/~wlawvere Prev by Date: categories: Preprint: a paper on injective hulls Next by Date: categories: Functorial injective hulls Prev by thread: categories: Topos theory and large cardinals Next by thread: categories: dom fibration Index(es): Date Thread

42. Topos Theory Seminar --- Fall 2003 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/butz/courses/TT-E2003.html

Topos Theory Seminar Fall 2003 Organizers: Lars Birkedal birkedal@itu.dk , Room 2.21, 3816 8868 Carsten Butz butz@itu.dk , Room 1.17, 3816 8820 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 we plan to pause and read parts of Lambek/Scott: Introduction to higher order categorical logic Cambridge University Press 1986; and Mac Lane/Moerdijk: Sheaves in Geometry and Logic Springer-Verlag 1992. Additional material can be found in Jaap van Oosten's notes on Basic Category Theory . Focus will be on Lambek/Scott. To gain credit for this 7.5 ECTS seminar you have to participate actively in the discussions. Moreover, you have to take responsibility for at least one topic, stretching usually over more than a week. Meeting time: We meet on Fridays, 14:0015:30, Room 2.55. Participants: Lars Birkedal (LB) Carsten Butz (CB) Volodya Shavrukov (VS) Thomas Hildebrandt (TH) (RM) Noah Torp-Smith (NTS) Nina Bohr (NB) Rasmus Lerchedahl Petersen (RLP) Bodil Biering (BB) Marie Bjerrum (MB) (birkedal@itu.dk, butz@itu.dk, volodya@itu.dk, hilde@itu.dk, mogel@itu.dk, noah@itu.dk, nina@itu.dk, m98rlp@math.ku.dk, bodil@math.ku.dk, m98mb@math.ku.dk)

43. [math/0608040] Higher Topos Theory Abstract This purpose of this book is twofold to provide a general introduction to higher category theory (using the formalism of quasicategories or weak Kan complexes ), and http://arxiv.org/abs/math/0608040

arXiv.org math 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: math new recent NASA ADS 13 blog links ... what is this? Bookmark what is this? Mathematics > Category Theory Title: Higher Topos Theory Authors: Jacob Lurie (Submitted on 2 Aug 2006 ( ), last revised 31 Jul 2008 (this version, v4)) Abstract: This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few applications to classical topology are included. Comments: 735 pages. An updated and expanded version of the earlier submission math.CT/0306109 2/10/07: Various minor additions and corrections; added some material on combinatorial model categories to the appendix. 3/8/7: Actually uploaded the update this time; added material on fiber products of higher topoi. 7/31/08: Several sections added, others rewritten Subjects: Category Theory (math.CT)

44. Lurie, J.: Higher Topos Theory (AM-170). of the book Higher Topos Theory (AM170) by Lurie, J., published by Princeton University Press...... http://press.princeton.edu/titles/8957.html

45. Lars Birkedal / Teaching / Topos Theory Seminar --- Spring 2003 This is a Ph.D. seminar in which we study aspects of topos theory relevant to computer science. This semester we plan to continue reading and discussing material from Peter http://www.it-c.dk/people/birkedal/teaching/topos-theory-Spring-2003/

Topos Theory Seminar Spring 2003 Organizers: Lars Birkedal birkedal@it-c.dk , Room 2.21, 3816 8868 Carsten Butz butz@it-c.dk , Room 1.17, 3816 8820 This is a Ph.D. seminar in which we study aspects of topos theory relevant to computer science. This semester we plan to continue reading and discussing material from Peter Johnstone's opus: Sketches of an Elephant: A Topos Theory Compendium . In the schedule below, readings refer to Johnstone's books. Meeting time: We meet on Fridays, 14:0015:30, Room 2.03 (except January 10: Room 2.55; February 7: Room 2.31, March 7: Room 2.55). Schedule: Date Speaker Reading Fri Jan CB A.4.2: Surjections and Inclusions Fri Jan LB A.4.3: Cartesian Reflectors and Sheaves Fri Jan LB A.4.3: Cartesian Reflectors and Sheaves Fri Jan VS A.4.4: Local Operators Fri Feb VS A.4.4: Local Operators Fri Feb REM A.4.5 (pages 204211, incl. 4.5.9): Examples of Local Operators Fri Feb REM A.4.5 (pages 211217, incl. 4.5.16): Examples of Local Operators Fri Feb LB A.4.5 (pages 217223): Examples of Local Operators

46. University Of Chicago Category Theory Seminar This quarter we will have a series of talks on topos theory, model categories, quasicategories, and higher topos theory. These current topics lie at the intersection of algebraic http://www.math.uchicago.edu/~fiore/1/categoryseminar.html

University of Chicago Category Theory Seminar We will have category theory talks Thursdays 3:00-4:20 in Eckhart 203 in the Proseminar . A rough schedule is there There will occasionally be category theory talks in the Topology Proseminar Eckhart 203 T Th 1:30-3:00. Check the calendar to see if there is a topology talk or category talk, or both. To request a future speaker or for questions, please contact Tom Fiore (fiore AT math.uchicago.edu). To sign up for electronic announcements of talks, please visit http://zaphod.uchicago.edu:8080/mailman/listinfo/category_theory_seminar Spring 2007 Talks Fall 2006 Talks Fall 2006 Plan This quarter we will have a series of talks on topos theory, model categories, quasicategories, and higher topos theory. These current topics lie at the intersection of algebraic geometry, algebraic topology, logic, and higher category theory, and should be of interest to a wider audience. References Topos Theory Goldblatt, Robert I. Topoi. Studies in Logic and the Foundations of Mathematics, 98. North-Holland Publishing Co., Amsterdam-New York, 1979. Johnstone, Peter T. Sketches of an elephant: a topos theory compendium. Vol. 1. Oxford Logic Guides, 43. The Clarendon Press, Oxford University Press, New York, 2002. xxii+468+71 pp.

47. Sketches Of An Elephant: A Topos Theory Compendium - Volume 2 Title Sketches of an Elephant A Topos Theory Compendium Volume 2 Authors Johnstone, Peter T. Publication Sketches of an Elephant A Topos Theory Compendium - Volume 2, by Peter http://adsabs.harvard.edu/abs/2002set2.book.....J

Sign on SAO/NASA ADS Physics Abstract Service Find Similar Abstracts (with default settings below Electronic On-line Article (HTML) Citations to the Article (74) Citation History ... Translate This Page Title: Sketches of an Elephant: A Topos Theory Compendium - Volume 2 Authors: Publication: Sketches of an Elephant: A Topos Theory Compendium - Volume 2, by Peter T Johnstone, pp. 715. Foreword by Peter T Johnstone. Oxford University Press, Nov 2002. ISBN-10: 0198515987. ISBN-13: 9780198515982 Publication Date: Origin: WEB Comment: ISBN: 9780198515982 Bibliographic Code: 2002set2.book.....J Abstract 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. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text. Bibtex entry for this abstract Preferred format for this abstract (see Preferences Find Similar Abstracts: Use: Authors Title Abstract Text Return: Query Results Return items starting with number

48. Topos Theory - Microsoft Academic Search discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. in section in section 2, we http://academic.research.microsoft.com/Search.aspx?query=topos theory

49. Topos Theory, Noncommutative Geometry, And Quantum Logic (www.narcis.nl) Title Topos theory, noncommutative geometry, and quantum logic Period 06 / 2009 06 / 2013 Status Current Dissertation Yes Data Supplier NWO http://www.narcis.info/research/RecordID/OND1336208/Language/en/

KNAW Narcis Back to search results Research Topos theory, noncommutative geometry, and quantum logic Pagina-navigatie: Main Title Topos theory, noncommutative geometry, and quantum logic Period Status Current Dissertation Yes Data Supplier: NWO Abstract Related organisations Secretariat Mathematical Physics (RU) Financier NWO Council for Physical Sciences (NWO) Related people Researcher Ing. S.A.M. Wolters Project leader Prof.dr. N.P. Landsman Update this data Go to Website Navigation: Home about narcis Nederlands Royal Netherlands Academy of Arts and Sciences Go to page top Go back to contents Go back to site navigation

50. Course In Topos Theory Topos Theory, spring term 1999. A graduate course (6 course points) in mathematical logic. http://www.math.uu.se/~palmgren/topos-eng.html

Topos Theory, spring term 1999 A graduate course (6 course points) in mathematical logic. Topos theory grew out of the observation that the category of sheaves over a fixed topological space forms a universe of "continuously variable sets" which obeys the laws of intuitionistic logic. These sheaf models, or Grothendieck toposes, turn out to be generalisations of Kripke and Beth models (which are fundamental for various non-classical logics) as well as Cohen's forcing models for set theory. The notion of topos was subsequently extended and given an elementary axiomatisation by Lawvere and Tierney, and shown to correspond to a certain higher order intuitionistic logic. Various logics and type theories have been given categorical characterisations, which are of importance for the mathematical foundations for programming languages. One of the most interesting aspects of toposes is that they can provide natural models of certain theories that lack classical models, viz. synthetic differential geometry. This graduate course offers an introduction to topos theory and categorical logic. In particular the following topics will be covered: Categorical logic: relation between logics, type theories and categories. Generalised topologies, including formal topologies. Sheaves. Pretoposes and toposes. Beth-Kripke-Joyal semantics. Boolean toposes and Cohen forcing. Barr's theorem and Diaconescu covers. Geometric morphisms. Classifying toposes. Sheaf models of infinitesimal analysis.

51. Higher Topos Theory (AM-170) (Adobe Reader) Ebook Higher Topos Theory (AM170) ebook plus Mathematics Advanced. Lurie, Jacob eBooks download at Diesel eBook Store in Adobe, ePub, Mobipocket, Microsoft and eReader http://www.diesel-ebooks.com/cgi-bin/item/9781400830558/Higher-Topos-Theory-AM-1

52. [haskell-art] Topos Theory And Music (Was: Welcome) haskellart Topos theory and music (Was welcome) Henning Thielemann Tue, 27 Feb 2007 082519 -0800 http://www.mail-archive.com/haskell-art@lists.lurk.org/msg00007.html

haskell-art Thread Date [haskell-art] Topos theory and music (Was: welcome) Henning Thielemann Tue, 27 Feb 2007 08:25:19 -0800 http://www.math.uni-bremen.de/Math-Net/pages/news/archives/SchedulesOfEvents_de-old.html using a Mac and Lisp and Topos theory and whatever for automatically answering musical questions, like "what is the meter of a given sequence of tones". http://flp.cs.tu-berlin.de/~noll/ http://lists.lurk.org/mailman/listinfo/haskell-art [haskell-art] Topos theory and music (Was: welcome) Henning Thielemann Reply via email to

53. Several Topos Theory Questions - MathOverflow Hey. I have a few off the wall questions about topos theory and algebraic geometry. Do the following few sentences make sense? Every scheme X is pinned down by its Hom functor Hom http://mathoverflow.net/questions/2314/several-topos-theory-questions

login faq how to ask meta ... Several Topos theory questions Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points Hey. I have a few off the wall questions about topos theory and algebraic geometry. Do the following few sentences make sense? Every scheme X is pinned down by its Hom functor Hom(-,X) by the yoneda lemma, but since schemes are locally affine varieties, it is actually just enough to look at the case where "-" is an affine scheme. So you could define schemes as particular functors from CommRing^op to Sets. In this setting schemes are thought of as sheaves on the "big zariski site". If that doesn't make sense my next questions probably do not either. 2 The category of sheaves on the big zariski site forms a topos T, the category of schemes being a subcategory. It is convenient to reason about toposes in their own "internal logic". Has there been much thought done about the internal logic of T, or would the logic of T require too much commutative algebra to feel like logic? Along these lines, have there been attempts to write down an elementary list of axioms which capture the essense of this topos? I am thinking of how Anders Kock has some really nice ways to think of differential geometry with his SDG. 3 What is it about the category of commutative rings which makes it possible to put such a nice site structure on it, but not other algebraic categories? Gluing rings together lead to huge advancements in algebraic geometry. What about gluing groups? Is there a nice Grothendieck topology you could put on Groups^op, and then you could start studying sheaves on this site? If not, why not - what about rings makes them so special?

54. Categories: Topos Theory And Large Cardinals To categories@mta.ca; Subject categories Topos theory and large cardinals; From Andrej.Bauer@cs.cmu.edu; Date 01 Mar 2000 222958 0500; Sender cat-dist@mta.ca http://north.ecc.edu/alsani/ct99-00(8-12)/msg00117.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Topos theory and large cardinals To categories@mta.ca Subject : categories: Topos theory and large cardinals From Andrej.Bauer@cs.cmu.edu Date : 01 Mar 2000 22:29:58 -0500 Sender cat-dist@mta.ca Source-Info : Sender is really andrej+@gs2.sp.cs.cmu.edu User-Agent : Gnus/5.0803 (Gnus v5.8.3) XEmacs/20.4 (Emerald) Can you complete this analogy? ``Large cardinals are to ZFC, as are to topos theory.'' One answer is "Grothendieck universes", but they correspond to rather small large cardinals. Can we go further than that? Andrej Bauer School of Computer Science Carnegie Mellon University http://andrej.com Prev by Date: categories: Johnstone review of Clark/Davey Next by Date: categories: dom fibration Prev by thread: categories: Johnstone review of Clark/Davey Next by thread: categories: Topos theory and large cardinals Index(es): Date Thread

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