81. Category Theory (mathematics) -- Britannica Online Encyclopedia category theory (mathematics), Email is the email address you used when you registered. Password is case sensitive. http://www.britannica.com/EBchecked/topic/99404/category-theory

document.write(''); Search Site: Advanced Search With all of these words With the exact phrase With any of these words Without these words Home SHOP BROWSE BLOG ... HELP Username: Password: Remember me Forgot your password? Help Email " is the e-mail address you used when you registered. Password " is case sensitive. If you need additional assistance, please contact customer support Enter the e-mail address you used when enrolling for Britannica Premium Service and we will e-mail your password to you. category-theory My Britannica CREATE MY category the... NEW ARTICLE ... SAVE category theory Table of Contents: category theory Article Article Related Articles Related Articles External Web sites External Web sites Citations Article Related Articles External Web sites Citations LINKS Related Articles Aspects of the topic category theory are discussed in the following places at Britannica. Assorted References major reference in foundations of mathematics: Category theory Category theory history of algebra in algebra (mathematics): Category theory The second attempt to formalize the notion of structure developed within category theory. The first paper on the subject was published in the United States in 1942 by Mac Lane and Samuel Eilenberg. The idea behind their approach was that the essential features of any particular mathematical domain (a category) could be identified by focusing on the interrelations among its elements, rather than...

82. Linear Logic In Computer Science TMR Network European TMR research network. http://iml.univ-mrs.fr/ldp/LINEAR/

83. Category Theory Category Theory. Arrows, Structures and Functors The Categorical Language. Category theory studies structural aspects of mathematics that are common to many fields of http://www.education.wichita.edu/alagic/nextpage/categories.htm

Category Theory 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.

84. SpringerLink - Applied Categorical Structures Contents from vol.3 (1995). http://www.springerlink.com/content/100235/

Username Password Remember Me Forgot your Password? Register Now Log In via Shibboleth or Athens SpringerLink Skip to Main Content Log In or Out Skip to Search springer.com ... springerprotocols.com Choose preferred language English Deutsch SpringerLink You have Guest access. What can I do as a guest? Search Basic Search Search For All Content Author or Editor Publication Volume Issue Page Advanced Search Content Search For Full Text Title Only DOI Author Editor Citation Publication (Title, DOI ISSN or ISBN Volume Issue Page Category and Date Limiters Content Category All Categories Only Journals Only Books Only Protocols Entire Range of Publication Dates Select date range Publication Dates Between Start Date AND End Date Order of Results Most Relevant First Most Recently Published First Alphabetical Home My SpringerLink Saved Items Favorites ... Mathematics and Statistics Applied Categorical Structures Volume 1 / 1993 - Volume 18 / 2010 Articles available before print publication Online First™ Viewing items 1 - 10 of 57 Journal About Search within Search Within This Journal Hide Filters Show Filters Browse This Journal Online First™ Open Access Samples Contemporary Content Volume 18 Number 5 / October 2010 Number 4 / August 2010 Number 3 / June 2010 ... Number 1 / March 1997 Archival Content Volume 4 / 1996 (3 Issues) Volume 3 / 1995 (4 Issues) Volume 2 / 1994 (4 Issues) Volume 1 / 1993 (4 Issues) Filter Results Remove criteria to expand these results Content Status > Online First™ Add criteria from below to refine these results

85. Categories John Baez and James Dolan, Categorification, in Higher Category Theory, eds. Ezra Getzler and Mikhail Kapranov, Contemp. Math. 230, American Mathematical Society, Providence http://www.math.ucr.edu/home/baez/categories.html

Categories, Quantization, and Much More John Baez April 12, 2006 Quantum theory can be thought of as the generalization of classical mechanics you get by dropping the assumption that observable quantities like position and momentum commute. In quantum theory one thus learns to like noncommutative, but still associative, algebras. It is interesting however to note why associativity without commutativity is studied so much more than commutativity without associativity. Basically, because most of our examples of binary operations can be interpreted as composition of functions. For example, if write simply x for the operation of adding x to a real number (where x is a real number), then x + y is just x composed with y. Composition is always associative so the + operation is associative! If we try to generalize the heck out of the concept of a group, keeping associativity as a sacred property, we get the notion of a category. Categories are some of the most basic structures in mathematics. They were created by Samuel Eilenberg and Saunders MacLane. In fact, MacLane said: "I did not invent category theory to talk about functors. I invented it to talk about natural transformations." Huh? Wait and see.

86. Robert Rosebrugh - Home Page Mount Allison University - Higher dimensional category theory, computational category theory and theory of database systems. http://www.mta.ca/~rrosebru/index.html

Robert Rosebrugh Professor of Mathematics and Computer Science and Programme Coordinator, Interdisciplinary B.Sc.(Aviation) at Mount Allison University in Sackville, NB, Canada. Email: rrosebrugh at mta dot ca. Here are some photos. Current times. Research Interests: higher dimensional category theory, computational category theory, theory of database systems. Publications: Articles available for download. Electronic Publishing: Managing Editor of the electronic journal on category theory: Theory and Applications of Categories Moderator of categories -the Internet mailing list on category theory. Software: Entity-Attribute Sketch Implementation Kit Java application - Version 2.0 (June 2009) mathcs.mta.ca/research/rosebrugh/Easik/ Graphical Database for Category Theory (GDCT) Java application - Version 3.0 (February 2006) mathcs.mta.ca/research/rosebrugh/gdct/ A Database of Categories - a menu-based C program (1995). Member of the Computational Category Theory Project For local information on the project see www.mta.ca/~rrosebru/compcat/compcat.html

87. CatMAT 2000 Categorical Methods in Algebra and Topology - Commemorating 25 years of Category Theory in Bremen. University of Bremen, Germany; 2125 August 2000. http://katmat.math.uni-bremen.de/catmat2000/

88. Category Theory - Article And Reference From OnPedia.com Category theory is a mathematical theory that deals in an abstract way with mathematical structures a http://www.onpedia.com/encyclopedia/category-theory

Category Theory Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "generalized abstract nonsense ". The phrase originated at a time when category theory was novel and some considered it too abstract to be useful or interesting. This derogatory designation was then co-opted by advocates of the new theory. In any case, the term should not be interpreted that category theory is nonsensical or non-rigourous ; indeed, an acquaintance with the basic notions of category theory is now considered part of the standard education of a mathematician , and category theory has even found applications in modern physics and theoretical computer science . See list of category theory topics for a breakdown of relevant articles. Background A category attempts to capture the essence of a class of related mathematical objects, for instance the class of groups . Instead of focusing on the individual objects (groups) as mathematical theories have traditionally done, category theory emphasizes the morphisms the structure-preserving maps between these objects. In the example of groups, these are the

89. School On Category Theory And Applications University of Coimbra, Portugal; 1317 July 1999. http://www.mat.uc.pt/~scta/

SCHOOL ON CATEGORY THEORY AND APPLICATIONS Department of Mathematics University of Coimbra PORTUGAL July 13-17, 1999 Welcome to the web site of the School on Category Theory and Applications, which will take place from Tuesday morning, 13 July 1999, through Saturday morning, 17 July, in Coimbra, Portugal. This school is being organized by the Category Theory Group of the University of Coimbra. Programme Timetable New! Organizing Committee Location Support Registration ... Universidade de Coimbra Apartado 3008 3000 Coimbra PORTUGAL Phone: +351-39-791150 Fax: +351-39-832568 E-mail: scta@mat.uc.pt Last updated: June 9, 1999 by Jorge Picado

90. Flipping Arrows In CoBurger King : Inside T5 Jul 14, 2010 Category theory crash course for the working Haskell programmer. . join is far more rooted in category theory (indeed, it defines the http://blog.ezyang.com/2010/07/flipping-arrows-in-coburger-king/

91. Category Theory Demonstrations Jocelyn Paine's Home Page Publications What might Categories do for AI and Cognitive Science? nCategory Caf thread about Graphical Category Theory Demonstrations http://www.j-paine.org/cgi-bin/webcats/webcats.php

92. 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 This page is provided for historical interest. For a list of recent and forth coming conferences hosted at Informatics in Edinburgh, see the page www.inf.ed.ac.uk/events/conferences/ 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

93. Applications Of Category Theory To Computer Science Mount Allison University, Sackville, NB, Canada; 812 June 1998. http://www.mta.ca/~cat-dist/ctss98/

Workshop: Applications of Category Theory to Computer Science June 8-12, 1998 Mount Allison University, Sackville, NB, Canada In conjunction with the Category Theory Session at the Canadian Mathematical Society's Summer 1998 Meeting, see camel.math.ca/CMS/Events/summer98/ , there will be a workshop on the Applications of Category Theory to Computer Science, directed towards graduate students and young researchers. The arrival day Sunday, June 7, 1998 - residence accommodation will be available from June 6. The invited instructors are M. Barr (McGill) and R.F.C. Walters (Sydney). Residence accommodation will be available at Mount Allison University at a cost of $27.60/person/night for a single room $24.30/person/night for a shared double room $23.00/person/night for either of the above for students upon presentation of a student card. (All prices are in Canadian dollars and include taxes.) Bookings can be made at http://www.mta.ca/conference/overnigh.htm There will be a registration fee of $50 for the workshop. To preregister send e-mail to ct95@mscs.dal.ca

94. OctoberFest 99: Centre De Recherche En Théorie Des Catégories -- Montréal McGill University, Montreal, Canada; 1617 October 1999. http://www.math.mcgill.ca/triples/octoberfest99.html

Category Theory Research Center Category Theory OctoberFest McGill University, Montreal Saturday - Sunday, October 16 - 17, 1999 The meeting is now over, but for information purposes, this page will remain in place for a while. Email addresses for the speakers may be found on the list of talks . "Provisional" schedules etc are now final. We invite you to join us in Montreal next October for a weekend meeting in Category Theory, the "not-quite-annual" OctoberFest. As has been the tradition with these meetings, we invite talks from all participants. If you wish to give a talk, send your request along with a short abstract (before the end of September please) to Robert Seely at the address below. The final schedule of talks will be handed out at the meeting, but a provisional schedule is available, as well as a provisional list of speakers , in the meantime. ( Also ABSTRACTS of selected talks.) We will meet in the Bronfman Building, 1001 Sherbrooke West, on Saturday morning, October 16th. Coffee will be available from 8:30 am. The first talk will be at 9:00. Registration will take place during the morning, before the first talk and during the first coffee break. Lectures will be in room BRON 151. There will be a registration fee of $CAN40 ($US30), $CAN20 ($US15) for students. There will be a dinner/party to be held Saturday evening, hosted by Marta Bunge. (Instructions for getting to the Bunge home will be announced at the meeting.) Please let us know if you intend to join us by sending a short email (before the end of September if possible) to

95. The Comonad.Reader » Category Theory About a year back I posted a field guide of recursion schemes on this blog and then lost it a few months later when I lost a couple of months of blog entries to a crash. http://comonad.com/reader/category/category-theory/

96. (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

97. The Universal Framework For Science And Engineering. Category Theory. Life becomes too trivial. Now, General relativity and Quantum mechanics are not extraordinary things. These theories are rather an everyday engineering tool. http://www.mathframe.com/articles/usef/categorytheory/index.html

Category theory. by Dr. Petr Ivankov Introduction Category Theory Project Downloads (Source code, Tutorial, Installer). Download sample of functors. Download sample of limits. Download sample of editor of objects. Life becomes too trivial. Now, General relativity and Quantum mechanics are not extraordinary things. These theories are rather an everyday engineering tool. For example, the usage of Computational chemistry enables us construct molecules like puzzles. However, very interesting physical theories are being developed now. Modern Superstring theory and M-theory are very exciting and complicated. Even scientists have no hope of practical applications for them now. Rather, they would like to understand the sense of these theories. This article is devoted to software that would be of help to advanced scientists. Background Modern physics uses lots of kinds of objects from different branches of math (see picture above). The Category theory provides interoperability between them. It is very abstract, and not all mathematicians recognize it. It is even called as Abstract nonsense . But it is no longer too abstract when my software uses its theorems. Moreover, I've found that any software devoted to advanced math should be based on the Category theory. It is clear that I've not included all branches of math into my software. It is a business for the whole of my life. Now, my software includes braches of math that are applicable for

98. Computational Category Category Theory Project Computational Category Theory Project group. People, activities, software. http://www.mcs.le.ac.uk/~ah83/compcat/

Contents Goals and Method Members of CompCat Developments and Information Links to CompCat Member Sites Universita dell' Insubria, Como, Italy Mt. Allison University, Sackville, New Brunswick, Canada School of Mathematics, University of Wales, Bangor, Wales Computing Department, Macquarie University, Sydney, Australia ... MCS, University of Leicester, England Up: Anne's Home page Computational Category Theory Project Goals and Method The aim of this project is the development of software on a wide variety of platforms for computing with mathematical categories and associated algebraic structures. Although writing on different platforms each group will undertake to make available programs for translating their input and output files to the formats of the other groups. Members R. F. C. Walters Universita dell' Insubria, Como, Italy Bob Rosebrugh Mt. Allison University, Sackville, New Brunswick, Canada ... MCS, University of Leicester, England Developments and Information Here is a link to the list of software and structure definitions To join the mailing list contact You might also like to visit: Author: Anne Heyworth Last updated: 2nd February 2001 Any opinions expressed on this page are those of the author.

99. Resources For Learning Category Theory - Stack Overflow Jun 26, 2010 I am going to take a course on category theory soon. is the blog category theory? seemed more like real analysis when I read it; http://stackoverflow.com/questions/1224491/resources-for-learning-category-theor

100. PlanetMath: Category Theory Introduction. Much of contemporary mathematics studies algebraic structures of one sort or another rings, groups, vector spaces and many others. More generally, the idea of a http://planetmath.org/encyclopedia/CategoryTheory.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About category theory (Topic) Introduction Much of contemporary mathematics studies algebraic structures of one sort or another: rings groups vector spaces and many others. More generally, the idea of a set with some structure is very general: topological spaces differentiable manifolds graphs and so on. Each of these kinds of things has a notion of a function that respects the structure: group and ring homomorphisms linear transformations continuous functions differentiable functions ... graph homomorphisms , and so on. In order to mathematically capture the notion of ``kind of thing'', as well as ``function which preserves the structure'', the notion of a category was introduced.

Page 5     81-100 of 128    Back | 1  | 2  | 3  | 4  | 5  | 6  | 7  | Next 20