Geometry.Net - Pure_And_Applied_Math: Category Theory

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/

Extractions: Fall 2001 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 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.
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/

Extractions: Secretary: Baker 135 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.
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

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

Extractions: URL "http://www.disi.unige.it/conferences/ctcs97/" CTCS'99 (Edinburgh) 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
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

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

Extractions: 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:
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

Extractions: 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
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

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

Extractions: 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
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/
(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/

Extractions: 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
Category Theory And Homotopy Theory
School of Informatics, category theory and Homotopy Theory.Category Science Math Topology Research GroupsUniversity 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

Extractions: Personnel: 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.
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

Extractions: 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. INTAS grant: Algebraic homotopy, Galois theory and Descent
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
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

Extractions: 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. 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.
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/
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

Extractions: 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.
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/

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