41. Lars Birkedal / Teaching / Category Theory Project --- Fall 2001 category theory Project Fall 2001. A number of applications of category theory tocomputer science will also be covered, including some recent developments. http://www.itu.dk/people/birkedal/teaching/category-theory-Fall-2001/

Category Theory Project Fall 2001 Instructors: Lars Birkedal birkedal@it-c.dk , Glentevej 67, Room 2.21, 3816 8868 Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science, where it for example has been used to describe and analyse models of both sequential and parallel programming languages. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This project is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines. A number of applications of category theory to computer science will also be covered, including some recent developments. Project Information Project format We have a common project meeting each week, where we discuss the reading material. Project participants have to write a report, on a topic of their own choice related to the reading material. Reports should preferable be written in groups with minimum 2, preferably 3, persons in each group.

42. Category Theory category theory. 80413/713. Overview. category theory, a branch of abstract algebra,has found many applications in mathematics, logic, and computer science. http://www.andrew.cmu.edu/course/80-413-713/

Category Theory Spring 2002 Course Information Place: BH 237B Time: TR 12 - 1:20 Instructor: Steve Awodey Office: Baker 152 (mail: Baker 135) Office Hour: Wednesday 2-3, or by appointment Phone: 8947 Email: awodey@andrew Secretary: Baker 135 Overview Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This course is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines. To be followed by a Fall course on categorical logic. Prerequisites Some familiarity with abstract algebra or logic. Texts Borceux, F.: Handbook of Categorical Algebra (Encyclopedia of Mathematics and its Applications). Cambridge University Press, 1994.

43. Category Theory For Computing Science send email to Charles Wells category theory for Computing Science.by Michael Barr and Charles Wells. Third Edition, now available http://www.cwru.edu/artsci/math/wells/pub/ctcs.html

Charles Wells' Home Page CWRU Mathematics Department Home Page send email to Charles Wells Category Theory for Computing Science by Michael Barr and Charles Wells. Third Edition, now available from Centre de recherches mathématiques (or by email to sales@crm.umontreal.ca ). This edition contains all the material dropped from the second edition (with corrections) and the answers to all the exercises. It is cheaper, too; it costs only about US$31, postpaid (surface mail) anywhere in the world. About earlier editions Some of the chapters in the first edition were dropped from the second edition in order to make room for new material. Revised and corrected versions of the omitted chapters may now be found in an electronic supplement to the text. We also provide corrections and additions to the first edition and corrections to the second edition send email to Charles Wells Charles Wells' Home Page CWRU Mathematics Department Home Page ... Unauthorized use prohibited window.open=NS_ActualOpen; window.open=NS_ActualOpen;

44. CTCS97 7th conference on category theory and Computer Science. S. Margherita Ligure, Italy; 46 September 1997. http://www.disi.unige.it/conferences/ctcs97/

CTCS'97, 4-6 September 1997, S. Margherita Ligure, Italy URL "http://www.disi.unige.it/conferences/ctcs97/" CTCS'99 (Edinburgh) Conference Programme and Abstracts of accepted papers Travel Information List of Participants CTCS'97 is the 7th conference on Category Theory and Computer Science . The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory, algebra, geometry and logic. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. The proceedings will be published by Springer as volume 1290 in the LNCS series. The conference will take place at Hotel Regina Elena , a 4 stars hotel with private beach, located in S. Margherita Ligure . This is a beautiful sea resort in Liguria very close to Portofino promontory and about 30 km east of Genova Programme committee S. Abramsky Edinburgh (UK) P.-L. Curien LIENS (France) P. Dybjer Chalmers (Sweden) P. Johnstone Cambridge (UK) G. Longo

45. Category Theory Definitions category theory Definitions. My plan is to decompose into their constituent definitionsa number of famous ideas from category theory as I study the subject. http://www.cs.tcd.ie/Robert.Byrne/CategoryTheoryDefns.html

Category Theory Definitions Semistrict n-categories (or "teisi") A theoretician of "n" Considered conditions on when Some mathematicians Could find definitions For n even greater than ten. - Lisa Raphals A B C D ... Z This dictionary is in development and has definitions under the following letters: A, C, D, E, F, I, K, M, N and S. Check the notation page for some notes. I have experimented with the Symbol font there but only use it for Greek letters in the definitions. My plan is to decompose into their constituent definitions a number of famous ideas from category theory as I study the subject. Some obvious examples are: monad, Kleisli category of monad, Kan extension, n-category, Yoneda lemma... along with the basic building blocks of functors, natural transformations... The main references are: Conceptual mathematics: a first introduction to categories . W. Lawvere and S. Schanuel 1997. Cambridge University Press. Categories for the Working Mathematician . S. Mac Lane 1998. Springer-Verlag. Sheaves in Geometry and Logic: A First Introduction to Topos Theory . S. Mac Lane and I. Moerdijk 1992. Springer-Verlag. Maintained by Robert Byrne

46. CTCS99 8th conference on category theory and Computer Science. Edinburgh, Scotland, UK; 1012 September 1999. http://www.dcs.ed.ac.uk/home/ctcs99/

Call for participation CTCS'99, 10-12 September 1999, Edinburgh, Scotland CTCS '99 is the 8th conference on Category Theory and Computer Science . The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. Previous meetings have been held in Guildford (Surrey), Edinburgh, Manchester, Paris, Amsterdam, Cambridge, and S. Margherita Ligure (Genova). Conference proceedings will appear in Electronic Notes in Theoretical Computer Science . Paper copies of the proceedings will be available to participants at the conference. Invited speakers: R. Hasegawa , Univ. of Tokyo (Japan) P. Freyd , Univ. of Pennsylvania (USA) M. Fiore , Univ. of Sussex (UK) D. Smith , Kestrel Institute (USA) Programme committee: J. Adamek TU Braunschweig (Germany) N. Benton Microsoft Res., Cambridge (UK) R. Blute U. Ottawa (Canada) T. Coquand Chalmers (Sweden) M. Escardo

47. Foundations And Methods Links: Category Theory category theory. category theory Mailing list with archive andmany relevant links including conferences; Practical Foundations http://www.cs.tcd.ie/Robert.Byrne/CategoryTheory.html

Category Theory Category Theory - Mailing list with archive and many relevant links including conferences Practical Foundations of Mathematics (online book) Basic Category Theory document based on an introductory course on category theory Computational Category Theory Project A brief description of category theory Category Theory Definitions Course on Coalgebras and Modal Logic ... Findings in Mathematical Physics includes discussion of category theory and applications, check weeks 29, 35, 49

48. Mbox: Re: Mechanization Of Category Theory Re Mechanization of category theory. HAGIYA He formally proved fundamentaltheorems on category theory up to Yoneda's Lemma. The http://www-unix.mcs.anl.gov/qed/mail-archive/volume-3/0138.html

Re: Mechanization of category theory HAGIYA Masami hagiya@is.s.u-tokyo.ac.jp Fri, 22 Mar 1996 18:08:30 +0900 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: David Rydeheard: "Re: Mechanization of category theory" Previous message: Bernd Ingo Dahn: "Re: Mechanization of category theory" In reply to: Bernd Ingo Dahn: "Re: Mechanization of category theory" Next in thread: David Rydeheard: "Re: Mechanization of category theory" We also have a thesis by an undergraduate student. He formally proved fundamental theorems on category theory up to Yoneda's Lemma. The purpose of the thesis was to compare formalization by set theory (in Mizar) and formalization by type theory. ftp://nicosia.is.s.u-tokyo.ac.jp/pub/staff/mohri/ST.ps Masami Hagiya (University of Tokyo) "On Formalization of Category Theory" by Takahisa Mohri (in March 1995) Abstract Category theory is important in several areas of computer science, such as semantics and implementation of functional and imperative programming languages, the design of programs, typing, et. On the other hand, in reserches called formalized mathematics, various areas of mathematics are formalized and formal proofs are checked on computers. Category theory is also one of the objects of these researches. In this paper, we compare the advantage and disadvantage of these formalizations. In particular, in advanced category theory including notions of functor category,set-valued functor, etc., the ability to deal with higher-order concepts and notions of sets is necessary. From this point of view, as an example, we attempt to prove Yoneda's Lemma based on each formalization.

49. Mbox: Mechanization Of Category Theory Mechanization of category theory. Clemens Ballarin Has anybody experiencein mechanizing category theory or knows of such work? I'm http://www-unix.mcs.anl.gov/qed/mail-archive/volume-3/0133.html

Mechanization of category theory Clemens Ballarin Clemens.Ballarin@cl.cam.ac.uk Thu, 21 Mar 1996 16:11:48 +0100 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Vaughan Pratt: "Re: Mechanization of category theory" Previous message: Lawrence C Paulson: "practical Proof Checking" Next in thread: Vaughan Pratt: "Re: Mechanization of category theory" Has anybody experience in mechanizing category theory or knows of such work? I'm about to implement basic parts of category theory in a tactical theorem prover based on higher order logic. I would appreciate to learn from anybody's earlier experiences. Thanks in advance, Clemens Next message: Vaughan Pratt: "Re: Mechanization of category theory" Previous message: Lawrence C Paulson: "practical Proof Checking" Next in thread: Vaughan Pratt: "Re: Mechanization of category theory"

50. CRTC -- Montréal -- Seminars Timetable. http://www.math.mcgill.ca/rags/seminar/

Category Theory Research Center Seminars scheduled in 2002-2003 Tuesday, 1 October 2002 3:30 - 5:00 M Barr Epimorphisms in rings of functions (Abstract) NOTE: We shall have coffee before the talk, at 2:30, this week. Tuesday, 8 October 2002 2:30 - 4:00 Daniele Bargelli Computational Approach to Arabic Conjugation Tuesday, 15 October 2002 3:30 - 5:00 Jean Malgoire (University of Montpellier) VERS UNE THEORIE DES FORMES (TOPOLOGIQUES) (Abstract) Tuesday, 22 October 2002 2:30 - 4:00 Mark Weber Trees, higher categories and operads (ABSTRACT) Tuesday, 29 October 2002 2:30 - 4:00 Marta Bunge Stack completions revisited (Abstract) Tuesday, 5 November 2002 2:30 - 4:00 Ivan Ivanov Remarks on (oldstyle) Ludics Tuesday, 12 November 2002 2:30 - 4:00 M Barr HSP subcategories of Eilenberg-Moore algebras (ABSTRACT) Tuesday, 19 November 2002 2:30 - 4:00 J. Egger (U Ottawa) Adherence Spaces Tuesday, 26 November 2002

51. Category Theory And Computer Science 1989 dblp.unitrier.de 3. category theory and Computer Science 1989 Manchester,UK. David H. Pitt, David E. Rydeheard, Peter Dybjer, Andrew http://www.informatik.uni-trier.de/~ley/db/conf/ctcs/ctcs89.html

Category Theory and Computer Science 1989: Manchester, UK David H. Pitt David E. Rydeheard Peter Dybjer Andrew M. Pitts (Eds.): Category Theory and Computer Science, Manchester, UK, September 5-8, 1989, Proceedings. Lecture Notes in Computer Science 389 Springer 1989, ISBN 3-540-51662-X DBLP Giuseppe Longo : Coherence and Valid Isomorphism in Closed Categories - Applications of Proof Theory to Category Theory In a Computer Scientist Perspective. 1-4 Ugo Montanari Daniel Yankelevich : An Algebraic View of Interleaving and Distributed Operational Semantics for CCS. 5-20 Ross Casley Roger F. Crew Vaughan R. Pratt : Temporal Structures. 21-51 Eugene W. Stark : Compostional Relational Semantics for Indeterminate Dataflow Networks. 52-74 Luca Cardelli John C. Mitchell : Operations in Records. 75-81 John Hughes : Projections for Polymorphic Strictness Analysis. 82-100 Eugenio Moggi : A Category-theoretic Account of Program Modules. 101-117 G. C. Wraith : A Note on Categorical Datatypes. 118-127 Kent Petersson Dan Synek Thomas Streicher : Independence Results for Calculi of Dependent Types. 141-154 Paul Taylor : Quantitative Domains, Groupoids and Linear Logic. 155-181

52. Category Theory And Computer Science category theory and Computer Science. 7. CTCS 1997 Santa Margherita Ligure,Italy. 3. category theory and Computer Science 1989 Manchester, UK. http://www.informatik.uni-trier.de/~ley/db/conf/ctcs/

Category Theory and Computer Science 7. CTCS 1997: Santa Margherita Ligure, Italy Eugenio Moggi Giuseppe Rosolini (Eds.): Category Theory and Computer Science, 7th International Conference, CTCS '97, Santa Margherita Ligure, Italy, September 4-6, 1997, Proceedings. Lecture Notes in Computer Science 1290 Springer 1997, ISBN 3-540-63455-X Contents 6. CTCS 1995: Cambridge, UK David H. Pitt David E. Rydeheard Peter Johnstone (Eds.): Category Theory and Computer Science, 6th International Conference, CTCS '95, Cambridge, UK, August 7-11, 1995, Proceedings. Lecture Notes in Computer Science 953 Springer 1995, ISBN 3-540-60164-3 Contents 5. CTCS 1993 4. CTCS 1991: Paris, France David H. Pitt Pierre-Louis Curien Samson Abramsky Andrew M. Pitts ... David E. Rydeheard (Eds.): Category Theory and Computer Science, 4th International Conference, Paris, France, September 3-6, 1991, Proceedings. Lecture Notes in Computer Science 530 Springer 1991, ISBN 3-540-54495-X Contents 3. Category Theory and Computer Science 1989: Manchester, UK David H. Pitt

53. (Canada) University Of Calgary Calgary Peripatetic Research Group in Logic and category theory alternates between departments of mathematics, philocophy, and computer science; meets weekly. http://pages.cpsc.ucalgary.ca/~luigis/CPRGLCC/

Calgary Peripatetic Research Group on Logic and Category Theory Meetings on Logic and Category Theory to be held in the Philosophy Mathematics and Computer Science Departments of the University of Calgary TIME: Monday 2:10pm (weekly) , PLACE: ICT 616 (or as arranged). Fall 2001: next seminar, incoming seminars, past seminars. Participants For talk titles, abstracts, comments etc. contact Luigi Santocanale

54. Category Theory And Homotopy Theory School of Informatics, category theory and Homotopy Theory.Category Science Math Topology Research Groups......University of Wales, Bangor School of Informatics Research Groups.category theory Homotopy Theory. Personnel Prof Tim Porter; Prof http://www.informatics.bangor.ac.uk/public/mathematics/research/cathom/cathom1.h

University of Wales, Bangor School of Informatics Research Groups Personnel: Prof Tim Porter Prof Ronnie Brown Mr Alinor Abdul Kadir Mr Magnus Forrester-Barker Collaborators: Prof Heiner Kamps Prof George Janelidze (Georgia) Dr Manuela Sobral (Coimbra) Dr Manuel Bullejos Prof Tony Bak (Bielefeld) Dr Gabriel Minian (Max Planck, Bonn) Introduction: Category theory was introduced in 1947 to give a richer language than that of set theory, which would be better able to express the structures of homotopy and homology theory then being revealed in the work of Cartan, Eilenberg, Mac Lane, Whitehead and others. In addition to the objects in a category (corresponding to the elements in a set), one also has arrows or "morphisms" between them. Thus for instance the collection of all sets and functions between them forms a category, the category of sets. This language and theory was soon found to have great usefulness in other branches of pure mathematics such as algebra, algebraic geometry, logic and more recently in computer science. The basic areas of research in category theory at Bangor are directed towards achieving a greater understanding of the categorical structure and interrelationships between the various objects studied by algebraic topology and homological algebra. Recent work in these areas has resulted in a large group of fascinating new structures. These have not yet revealed all their categorical structure nor have all the potential applications of these objects been fully investigated.

55. Category Theory And Homotopy Theory category theory Homotopy Theory, School of Informatics. Personnel Prof TimPorter; Prof Ronnie Brown; Mr Alinor Abdul Kadir; Mr Magnus ForresterBarker. http://www.informatics.bangor.ac.uk/public/mathematics/research/cathom/cathom1.s

Personnel: Prof Tim Porter Prof Ronnie Brown Mr Alinor Abdul Kadir Mr Magnus Forrester-Barker Collaborators: Prof Heiner Kamps Prof George Janelidze (Georgia) Dr Manuela Sobral (Coimbra) Dr Manuel Bullejos Prof Tony Bak (Bielefeld) Dr Gabriel Minian (Max Planck, Bonn) Introduction: Category theory was introduced in 1947 to give a richer language than that of set theory, which would be better able to express the structures of homotopy and homology theory then being revealed in the work of Cartan, Eilenberg, Mac Lane, Whitehead and others. In addition to the objects in a category (corresponding to the elements in a set), one also has arrows or "morphisms" between them. Thus for instance the collection of all sets and functions between them forms a category, the category of sets. This language and theory was soon found to have great usefulness in other branches of pure mathematics such as algebra, algebraic geometry, logic and more recently in computer science. The basic areas of research in category theory at Bangor are directed towards achieving a greater understanding of the categorical structure and interrelationships between the various objects studied by algebraic topology and homological algebra. Recent work in these areas has resulted in a large group of fascinating new structures. These have not yet revealed all their categorical structure nor have all the potential applications of these objects been fully investigated. Current Projects: INTAS grant: Algebraic homotopy, Galois theory and Descent

56. No Match For Category Theory No match for category theory. Sorry, the term category theory is not in the dictionary.Check the spelling and try removing suffixes like ing and -s . http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?category theory

57. Category Theory category theory. However, soon category theory became a field in itself. The reasonfor this is that it provides a unifying mathematical modeling language. http://education.twsu.edu/alagic/nextpage/categories.htm

Category Theory Mara Alagic Arrows, Structures and Functors: The Categorical Language Category theory studies structural aspects of mathematics that are common to many fields of mathematics: e.g., algebra, topology, functional analysis, logic, and computer science. Thus, category theorists tend to have many diverse interests. My research interests have included: relational categories, categories of some abstract structures and categorical semantics of programming languages. A Brief History of Category Theory Category theory is a mathematical language which arose in the study of limits for universal coefficient theorems in Cech cohomology by Eilenberg and Mac Lane (1942); so the topic has its origins in some sophisticated topology. However, soon category theory became a field in itself. The reason for this is that it provides a unifying mathematical modeling language. It lends itself very well to extracting and generalizing elementary and essential notions and constructions from many mathematical disciplines. Thanks to its general nature, the language of category theory enables one to "transport" problems from one area of mathematics, via suitable "functors", to another area, where the solution may be easier to find. Categories have successfully been applied in formulating and solving problems in topology, algebra, geometry and functional analysis. Moreover, in the sixties Lawvere started a project aiming at a purely categorical foundation of all mathematics, beginning with an appropriate axiomatization of the category of sets. This has led to a huge interest in and development of sheaf and topos theory.

58. KLUWER Academic Publishers | Category Theory, Homological Algebra Home » Browse by Subject » Mathematics » Foundations, Sets andCategories » category theory, Homological Algebra. Sort listing http://www.wkap.nl/home/topics/J/4/4/

Title Authors Affiliation ISBN ISSN advanced search search tips Home Browse by Subject ... Foundations, Sets and Categories Category Theory, Homological Algebra Sort listing by: A-Z Z-A Publication Date Abelian Groups and Modules Alberto Facchini, Claudia Menini October 1995, ISBN 0-7923-3756-5, Hardbound Price: 259.50 EUR / 328.50 USD / 198.00 GBP Add to cart Applications of Category Theory to Fuzzy Subsets November 1991, ISBN 0-7923-1511-1, Hardbound Price: 191.50 EUR / 241.50 USD / 145.75 GBP Add to cart Approximation Theorems in Commutative Algebra Classical and Categorical Methods September 1992, ISBN 0-7923-1948-6, Hardbound Price: 215.50 EUR / 273.00 USD / 164.75 GBP Add to cart Automata and Algebras in Categories August 1990, ISBN 0-7923-0010-6, Hardbound Printing on Demand Price: 342.50 EUR / 434.00 USD / 261.25 GBP Add to cart Basic Concepts of Synthetic Differential Geometry February 1996, ISBN 0-7923-3941-X, Hardbound Price: 193.50 EUR / 244.00 USD / 147.75 GBP Add to cart Categorical Structure of Closure Operators With Applications to Topology, Algebra and Discrete Mathematics D. Dikranjan, W. Tholen October 1995, ISBN 0-7923-3772-7, Hardbound

59. KLUWER Academic Publishers | Applications Of Category Theory To Fuzzy Subsets Books » Applications of category theory to Fuzzy Subsets. Applicationsof category theory to Fuzzy Subsets. Add to cart. edited by http://www.wkap.nl/prod/b/0-7923-1511-1

Title Authors Affiliation ISBN ISSN advanced search search tips Books Applications of Category Theory to Fuzzy Subsets Applications of Category Theory to Fuzzy Subsets Add to cart edited by Stephen Ernest Rodabaugh Youngtown State University, OH, USA Erich Peter Klement Institute of Mathematics, Johannes Kepler University, Linz, Austria Book Series: THEORY AND DECISION LIBRARY B: Mathematical and Statistical Methods Volume 14 Applications of Category Theory to Fuzzy Subsets is the first major work to comprehensively describe the deeper mathematical aspects of fuzzy sets, particularly those aspects which are category-theoretic in nature, and is intimately related to the first eleven years of the renowned International Seminar on Fuzzy Set Theory. Though it brings the reader to the very frontier of the mathematics of fuzzy set theory, its extensive bibliography, indices, and the tutorial nature of its longer chapters also make it suitable as a text for advanced graduate students. Part I develops model-theoretic foundations for fuzzy set theory, and in doing so, comprises an extensive study of monoid-valued sets, sheaves over commutative cl-monoids, weak and quasi topoi, local existence in such settings, and categories with two closed structures, including the logic and inference rules in these latter categories for the unbalanced subobjects modeling fuzzy subsets. Part II refines and works within non-model-theoretic approaches to fuzzy sets, giving a full account of the use of categorical methods to describe fuzzy topology from the structure-theoretic, category-theoretic, and point-set lattice-theoretic viewpoints. Explored in detail are set functors, topological constructs, convergence, and the relationship between locales, fuzzy topologies, and functor categories.

60. Category Theory For Computer Science category theory for Computer Science. Autumn 2002 computer sciencecategory theory in programming language semantics and design. http://www.daimi.au.dk/~nygaard/CTfCS/

Category Theory for Computer Science Autumn 2002 - Department of Computer Science University of Aarhus News Lectures ... People News The course has terminated. Merry Christmas! Lectures Mondays, 12-14 in the r3 meeting room. December 9th A coalgebraic treatment of automata. Presented by Saurabh Agarwal. December 2nd Infinite data structures, coalgebra, and coinduction. Presented by Michael Westergaard ( slides November 25th Finite data structures, algebra, and induction. Presented by Henning Korsholm Rohde ( slides November 18th Transition systems generalised into presheaves. Presented by Marco Carbone. November 11th Exercises related to last week's lecture. Designing subtyping disciplines in programming languages. Presented by Branimir Lambov. November 4th Exercise related to last week's lecture. Effects in functional programming handled by monads. Presented by Karl Kristian Krukow ( slides October 28th Modelling recursive types. Presented by Mads Sig Ager (

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