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         Topos Theory:     more books (19)
  1. Model Theory and Topoi (Lecture Notes in Mathematics)
  2. Diario de Un Skin: Un Topo En El Movimiento Neonazi Espanol (Spanish Edition) by Antonio Salas, 2003-01
  3. Another Sheaf by John Galsworthy, 2010-06-16
  4. Another Sheaf by John Galsworthy, 2010-10-24
  5. Regular Category: Category Theory, Limit, Coequalizer, Abelian Category, First-Order Logic, Complete Category, Morphism, Pullback, Epimorphism, Category of Sets, Topos, Ring Homomorphism

21. Topos Theory Seminar
This is an advanced Ph.D......Home Forskning PhD studies Courses topos theory Seminar, E2002,topos theory Seminar.
http://www.it-c.dk/Internet/research/phd/courses/TTS/
Hjem Nyhedsbrev Søg Find person ... Courses Topos Theory Seminar, E2002
Topos Theory Seminar
Description:
This is an advanced Ph.D. course, in which we read and present material from Peter Johnstone's new book
Sketches of an Elephant: A topos theory compendium. This semester we cover the chapters on Allegories and exact completions, and on Geometric morphisms of toposes. Meetings:
Fridays 14-15:30, Room 2.03. Credits: 7,5 ECTS.
Ph.D. students who wish to take the course for credit should prepare lectures and present the prepared material at least twice during the semester.
Opdateret 20/02-2003

22. AMCA: Covering Morphisms In Topos Theory Presented By Marta Bunge
Covering morphisms in topos theory by Marta Bunge Department of Mathematicsand Statistics, McGill University, Montreal, Canada
http://at.yorku.ca/cgi-bin/amca/cajf-21
AMCA Document # cajf-21 Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, Ontario, Canada Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich, Walter Tholen, York University
View Abstracts
Conference Homepage Covering morphisms in topos theory
by
Marta Bunge
Department of Mathematics and Statistics, McGill University, Montreal, Canada In the work of Janelidze in 1990, a formal notion of covering morphism arises from an abstract categorical framework given by a pair of adjoint functors. Associated with any such class of covering morphisms, there is a corresponding (pure) Galois theory, of which there are examples in different areas of mathematics. In topos theory, the class of all covering projections (local homeomorphisms determined by a locally constant object of the topos) that appears explicitly in the work of Barr and Diaconescu in 1981, has been shown already by Janelidze to be an instance of the above notion of covering morphism, but only under the conditions that either the base topos be Set (that is, for Grothendieck toposes), or else where the splitting cover in the topos is assumed connected. U (E) is defined by means of the pushout, in the 2-category

23. AMCA: Spectral Decomposition Of Ultrametric Spaces And Topos Theory Presented By
Homepage. Spectral Decomposition of Ultrametric Spaces and topos theoryby Alex J. Lemin Moscow State University of Civil Engineering
http://at.yorku.ca/cgi-bin/amca/cacl-81
AMCA Document # cacl-81 1999 Summer Conference on Topology and its Applications
August 4-7, 1999
C.W. Post Campus of Long Island University
Brookville, NY, USA Organizers
Sheldon Rothman, Ralph Kopperman
View Abstracts
Conference Homepage Spectral Decomposition of Ultrametric Spaces and Topos Theory
by
Alex J. Lemin
Moscow State University of Civil Engineering We consider categories M E T R and M E T R c U L T R A M E T R and U L T R A M E T R c of ultrametric spaces and the same maps. Given a family of ultrametric spaces, we prove that sums and products, equalizer and co-equalizer, pull-back and push-out, limits of direct and inverse spectra, if exist, are ultrametric. A product and a limit of inverse spectrum of complete metric spaces are complete. A space (X,d) is uniformly discrete 'for all' x, y X. This is necessarily complete.
Theorem Every complete ultrametric space is isometric to a limit of a countable inverse spectrum of uniformly discrete ultrametric spaces (and vise versa) (see [1]).
Corollary 1 Every compact ultrametric space is isometric to a limit of inverse sequence of skeletons of finite dimensional isosceles simplexes lying in Euclidean spaces (see [2]).

24. Homotopical Algebraic Geometry I Topos Theory, By Bertrand Toen And Gabriele Vez
Homotopical Algebraic Geometry I topos theory, by Bertrand Toen andGabriele Vezzosi. This is the first of a series of papers devoted
http://www.math.uiuc.edu/K-theory/0579/
Homotopical Algebraic Geometry I Topos theory, by Bertrand Toen and Gabriele Vezzosi

Bertrand Toen
Gabriele Vezzosi

25. Atlas: Covering Morphisms In Topos Theory By Marta Bunge
Covering morphisms in topos theory presented by Marta Bunge Departmentof Mathematics and Statistics, McGill University, Montreal, Canada
http://atlas-conferences.com/c/a/j/f/21.htm
Atlas Document # cajf-21 Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, Ontario, Canada Conference Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich and Walter Tholen, York University
View Abstracts
Conference Homepage Covering morphisms in topos theory
presented by
Marta Bunge
Department of Mathematics and Statistics, McGill University, Montreal, Canada In the work of Janelidze in 1990, a formal notion of covering morphism arises from an abstract categorical framework given by a pair of adjoint functors. Associated with any such class of covering morphisms, there is a corresponding (pure) Galois theory, of which there are examples in different areas of mathematics. In topos theory, the class of all covering projections (local homeomorphisms determined by a locally constant object of the topos) that appears explicitly in the work of Barr and Diaconescu in 1981, has been shown already by Janelidze to be an instance of the above notion of covering morphism, but only under the conditions that either the base topos be Set (that is, for Grothendieck toposes), or else where the splitting cover in the topos is assumed connected. U (E) is defined by means of the pushout, in the 2-category

26. Atlas: Spectral Decomposition Of Ultrametric Spaces And Topos Theory By Alex J.
Spectral Decomposition of Ultrametric Spaces and topos theory presentedby Alex J. Lemin Moscow State University of Civil Engineering
http://atlas-conferences.com/c/a/c/l/81.htm
Atlas Document # cacl-81 1999 Summer Conference on Topology and its Applications
August 4-7, 1999
C.W. Post Campus of Long Island University
Brookville, NY 11548, USA Conference Organizers
Sheldon Rothman and Ralph Kopperman
View Abstracts
Conference Homepage Spectral Decomposition of Ultrametric Spaces and Topos Theory
presented by
Alex J. Lemin
Moscow State University of Civil Engineering We consider categories M E T R and M E T R c U L T R A M E T R and U L T R A M E T R c of ultrametric spaces and the same maps. Given a family of ultrametric spaces, we prove that sums and products, equalizer and co-equalizer, pull-back and push-out, limits of direct and inverse spectra, if exist, are ultrametric. A product and a limit of inverse spectrum of complete metric spaces are complete. A space (X,d) is uniformly discrete 'for all' x, y X. This is necessarily complete.
Theorem Every complete ultrametric space is isometric to a limit of a countable inverse spectrum of uniformly discrete ultrametric spaces (and vise versa) (see [1]).
Corollary 1 Every compact ultrametric space is isometric to a limit of inverse sequence of skeletons of finite dimensional isosceles simplexes lying in Euclidean spaces (see [2]).

27. On Branched Covers In Topos Theory
On Branched Covers in topos theory. Jonathon Funk. We present somenew findings concerning branched covers in topos theory. Our
http://www.tac.mta.ca/tac/volumes/7/n1/7-01abs.html
On Branched Covers in Topos Theory
Jonathon Funk
We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox, of the including topos. We also have some new results concerning the general theory of KZ-doctrines, such as the closure under composition of discrete fibrations for a KZ-doctrine, in the sense of Bunge and Funk. Keywords: 1991 MSC: 18B25. Theory and Applications of Categories , Vol. 7, 2000, No. 1, pp 1-22.
http://www.tac.mta.ca/tac/volumes/7/n1/n1.dvi

http://www.tac.mta.ca/tac/volumes/7/n1/n1.ps

http://www.tac.mta.ca/tac/volumes/7/n1/n1.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n1/n1.dvi
...
TAC Home

28. Lars Birkedal / Teaching
Current Suggestions for Master's Theses topos theory Seminar Ph.D. seminar courseon topos theory. topos theory Seminar Ph.D. seminar course on topos theory.
http://www.itu.dk/people/birkedal/teaching/
Teaching
Current:
Suggestions for Master's Theses Topos Theory Seminar
Ph.D. seminar course on Topos Theory.
Spring 2002.
Past:
Advanced XML / Data on the Web
Fall 2002.
Topos Theory Seminar
Ph.D. seminar course on Topos Theory.
Fall 2002.
Models and Languages for Concurrency and Mobility
Spring 2002.
Distributed Systems
Spring 2002.
Topos Theory Seminar
Ph.D. seminar course on Topos Theory.
Spring 2002.
Reasoning about Resources (RaR) Seminar: Reasoning about Low-level Languages
Ph.D. seminar course on logics for reasoning about resources with a focus on reasoning about low-level languages, in particular languages with pointers and mutable data structures.
Fall 2001.
Topos Theory Seminar
Ph.D. seminar course on Topos Theory.
Fall 2001.
Category Theory Project
Introductory graduate project course on category theory.
Fall 2001.
Introductory Programming
Introductory programming course using Java.
Spring 2001.
Constructive Logic Project
Introductory graduate project on constructive logic.
Spring 2001.

29. HallPhilosophy.com Sketches Of An Elephant A Topos Theory
HallPhilosophy.com Sketches of an Elephant A topos theory Compendium(Oxford Logic Guides, 43 44). HallPhilosophy.com. the most
http://hallphilosophy.com/index.php/Mode/product/AsinSearch/019852496X/name/Sket

30. [gr-qc/9607069] Topos Theory And Consistent Histories: The Internal Logic Of The
34 +0100 (28kb) topos theory and Consistent Histories The InternalLogic of the Set of all Consistent Sets. Authors CJ Isham Comments
http://arxiv.org/abs/gr-qc/9607069
General Relativity and Quantum Cosmology, abstract
gr-qc/9607069
Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
Authors: C.J. Isham
Comments: 28 pages, LaTeX
Report-no: Imperial/TP/9596/55
Journal-ref: Int.J.Theor.Phys. 36 (1997) 785-814
Full-text: PostScript PDF , or Other formats
References and citations for this submission:
SLAC-SPIRES HEP
(refers to , cited by , arXiv reformatted);
CiteBase
(autonomous citation navigation and analysis)
Links to: arXiv gr-qc find abs

31. Categories: Topos Theory And Large Cardinals
categories topos theory and large cardinals. Andrej Bauer asked whether large cardinalsother than inaccessible ones have a natural definition in topos theory.
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
http://www.acsu.buffalo.edu/~wlawvere

32. Categories: Topos Theory And Large Cardinals
categories topos theory and large cardinals. To categories@mta.ca; Subjectcategories topos theory and large cardinals; From Andrej.Bauer@cs.cmu.edu;
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

33. Citations: Topos Theory - Johnstone (ResearchIndex)
Similar pages Partial morphisms in categories of effective objects Moggi ( Correct) 0.0 A Guided Tour in the Topos of Graphs - Sebastiano Vig Na (Correct)0.0 On Branched Covers In topos theory - Funk (2000) (Correct) Related
http://citeseer.nj.nec.com/context/13760/0
72 citations found. Retrieving documents...
Johnstone, P.T., Topos Theory , L.M.S. Monographs, vol. 10, Academic Press, 1977.
Home/Search
Document Not in Database Summary Related Articles Check
This paper is cited in the following contexts:
First 50 documents Next 50
Solving Recursive Domain Equations with Enriched Categories - Wagner (1994)
(14 citations) (Correct) ....However, the exposition should serve more as a reminder and a statement about notation than a first introduction to the concepts just listed. For that a much longer text is needed, and we refer the reader to the following list of core references. Fourman Scott 77] Mac Lane Moerdijk 92] Johnstone 77 ] Troelstra van Dalen 88] Wyler 91] Fourman 74] and also [Fourman 77] Rosolini 80] Ambler 92] and [Nawaz 85] The intention behind the notion of an m set is to model sets in a constructive universe with truth values in . Thus operations like equality (between members of sets) and ....
....on or internally, using logical connectives instead. We use the logic of forcing over , that is, the logic in h( For a good reference to forcing over a cHa, see [Troelstra van Dalen 88] volume II, and also in general for internal logic in a topos, for instance [Mac Lane Moerdijk 92] Johnstone 77 ] or [Fourman 74] 69 Definition 4.

34. Mathematical Topos - Wikipedia
The historical origin of topos theory is algebraic geometry. References John Baeztopos theory in a nutshell, http//math.ucr.edu/home/baez/topos.html.
http://www.wikipedia.org/wiki/Mathematical_topos
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Mathematical topos
From Wikipedia, the free encyclopedia. A topos (plural: topoi) in mathematics is a type of category which allows the formulation of all of mathematics inside it.
Introduction
Traditionally, mathematics is built on set theory , and all objects studied in mathematics are ultimately sets and functions . It has been argued that category theory could provide a better foundation for mathematics. By analyzing precisely which properties of the category of sets and functions are needed to express mathematics, one arrives at the definition of topoi, and one can then formulate mathematics inside any topos. Of course, the category of sets forms a topos, but that is boring. In more interesting topoi, the axiom of choice may no longer be valid, or the the

35. Untitled
Research Areas Category theory, topos theory, topology. It has natural connectionswith topos theory. See the Seminar of the Rough Set Technology Lab.
http://www.math.uregina.ca/~funk/research.html
Research Areas
Category theory, topos theory, topology
Current Research (newest to oldest)
Toposes and rough set theory: The idea of a rough set comes from computer science. It has natural connections with topos theory. See the Seminar of the Rough Set Technology Lab
Inverse semigroups and etendue: Joint with David Cowan.
Braid group orderings: Patrick Dehornoy has discovered that an Artin braid group carries a left-invariant linear ordering. In my article ``The Hurwitz action and braid group orderings,'' Theory and Applications of Categories , Vol. 9 (2001), No. 7, pp 121-150, a ramified covering space is used to find a linear ordering of a countably generated free group, which is not invariant under the product in the free group, and an action of the countably generated Artin braid group in the free group that preserves the ordering.
Cosheaf spaces and ramified covers: A theory of branched covers in topos theory, which is based on the ideas of Ralph Fox, is developed in ``On branched covers in topos theory,'' Theory and Applications of Categories , Vol. 7 (2000), pp 1-22. This approach uses complete spread geometric morphisms.

36. 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.

37. HallMathematics.com Sketches Of An Elephant A Topos Theory
HallMathematics.com Sketches of an Elephant A topos theory Compendium(Oxford Logic Guides, 43 44). HallMathematics.com. the
http://hallmathematics.com/index.php/Mode/product/AsinSearch/019852496X/name/Ske

38. Categorical Logic
Using sheaves, topos theory also subsumes Kripke semantics for intuitionisticlogic. Prerequisites. 80413/713 Category Theory, or equivalent.
http://www.andrew.cmu.edu/user/awodey/catlog/
Categorical Logic
Fall 2002
Course Information
Instructor: Steve Awodey
Office: Baker 152 (mail: Baker 135)
Office Hour: Thursday 1-2, or by appointment
Phone: 8947
Email: awodey@andrew
Secretary: Baker 135
Overview
This course focuses on applications of category theory in logic and computer science. A leading idea is functorial semantics, according to which a model of a logical theory is a set-valued functor on a structured category determined by the theory. This gives rise to a syntax-invariant notion of a theory and introduces many algebraic methods into logic, leading naturally to the universal and other general models that distinguish functorial from classical semantics. Such categorical models occur, for example, in denotational semantics. In this connection the lambda-calculus is treated via the theory of cartesian closed categories. Similarly higher-order logic is modelled by the categorical notion of a topos. Using sheaves, topos theory also subsumes Kripke semantics for intuitionistic logic.
Prerequisites
80-413/713 Category Theory, or equivalent.

39. Abstract:010801bunge
In this lecture I intend to introduce the notion of a (Fox complete)spread in topology and then in topos theory. This requires
http://www.maths.usyd.edu.au:8000/u/stevel/auscat/abstracts/010808bunge.html
Spreads and their completions
Marta Bunge (1/8/01)
The notion of a (complete) spread was introduced by R.H. Fox [6] in topology in order to give a common generalization of two different types of coverings with singularities (branched and folded). A different notion of a (proper) spread was given by E. Michael [10] in connection with topological cuts. In both cases, the basic ideas is that of a spread , meaning a continuous map p:Y>X , with Y locally connected, satisfying the property that the connected components (or more generally, the clopen subsets) of the p (U) , for U the opens of X , form a base for the topology of Y A topos-theoretic version of the notion of a spread was given by J. Funk and myself [3] as that of a geometric morphism p:F>E between toposes bounded over a base topos S , with F locally connected, for which there is a generating family a:f>p (E) of F over E which is an S-definable The two types of completions (Fox [6] and Micheal [10]) have a topos-theoretic counterpart, which, unlike the notion of a spread, are far from obvious. We deal with the Fox-like completion in [3] and with the Michael-type completion in [5]. An instance of complete spreads are the branched coverings, introduced in this context in [4] and (with minor variations) in [8]. On the other hand, the notion of folded cover has not been defined for toposes.

40. Subject Classification
61, SpringerVerlag (1968), 41-61. 19. Review of PM Cohn's Universal Algebra,2nd Edition, American Scientist (May-June 1982), 329. topos theory. 11.
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), 329.
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, Springer-Verlag (1972), 1-12 Continuously Variable Sets: Algebraic Geometry = Geometric Logic Proceedings of the Logic Colloquium , Bristol (1973), North Holland (1975), 135-157. Introduction to Part I of Model Theory and Topoi Springer Lecture Notes in Mathematics No.445

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