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         Topos Theory:     more books (19)
  1. Higher Topos Theory (AM-170) (Annals of Mathematics Studies) by Jacob Lurie, 2009-07-06
  2. The Topos of Music: Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola, 2003-01-17
  3. Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext) (Volume 0) by Saunders MacLane, Ieke Moerdijk, 1992-05-14
  4. Sketches of an Elephant: A Topos Theory Compendium 2 Volume Set (Oxford Logic Guides) by Peter T. Johnstone, 2003-07-17
  5. Topos Theory (London Mathematical Society Monographs, 10) by P.T. Johnstone, 1977-12
  6. Sketches of an Elephant: A Topos Theory Compendium Volume 2 (Oxford Logic Guides, 44) by Peter T. Johnstone, 2002-11-21
  7. Algebra in a Localic Topos With Application to Ring Theory (Lecture Notes in Mathematics 1038) by Francis Borceux, 1983-11
  8. Topos Theory: Grothendieck Topology
  9. Toposes, Triples and Theories (Grundlehren der mathematischen Wissenschaften) by M. Barr, C. Wells, 1984-12-20
  10. Algebra in a Localic Topos with Applications to Ring Theory (Lecture Notes in Mathematics) by F. Borceux, G. Van den Bossche, 1983-11-30
  11. Sketches of an Elephant: A Topos Theory Compendiumm vol. 1 (Oxford Logic Guides, 43) by Peter T. Johnstone, 2002-11-21
  12. An introduction to fibrations, topos theory, the effective topos and modest sets (LFCS report series) by Wesley Phoa, 1992
  13. Sketches of an Elephant: A Topos Theory Compendium. Vol. 1 by Peter T. Johnstone, 2002
  14. First Order Categorical Logic: Model-Theoretical Methods in the Theory of Topoi and Related Categories (Lecture Notes in Mathematics) (Volume 0) by M. Makkai, G.E. Reyes, 1977-10-05

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
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categories: Topos theory and large cardinals
http://www.acsu.buffalo.edu/~wlawvere

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: (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
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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
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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:
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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
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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/
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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
[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
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Several Topos theory questions
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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

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