Geometry.Net - Pure_And_Applied_Math: Category Theory

ATCAT
Dalhousie University, Halifax. Weekly meetings.Category Science Math Algebra category theory Research Groups@CAT. @CAT (Atlantic category theory Seminar) is our weekly seminar in which topicsrelated to category theory (algebra, logic, topology, category theory itself
http://www.mscs.dal.ca/~pare/atcat.html

Extractions: @CAT ( At lantic Cat egory Theory Seminar) is our weekly seminar in which topics related to category theory (algebra, logic, topology, category theory itself, etc.) are discussed. We meet on Tuesdays, starting at 2:30. Everyone is welcome. If you wish to be put on the mailing list, contact me at pare@mscs.cs.dal.ca 2002-2003 Participants
Category Theory - Wikipedia
category theory. From Wikipedia, the free encyclopedia. Category This isthe Gelfand representation. History of category theory. Categories
http://www.wikipedia.org/wiki/Category_theory

Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help From Wikipedia, the free encyclopedia. Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. Although originally developed in the context of algebraic geometry algebraic topology and universal algebra , it is now also used in various other branches of mathematics. Special categories called topoi can even serve as an alternative to set theory as the foundation of mathematics. Category theory is half-jokingly known as "abstract nonsense". 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 has been done traditionally, the
Limit (category Theory) - Wikipedia
Limit (category theory). In category theory, the limit of a functor generalizes thenotions of inverse limit and product used in various parts of mathematics.
http://www.wikipedia.org/wiki/Limit_(category_theory)

Extractions: Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help From Wikipedia, the free encyclopedia. In category theory , the limit of a functor generalizes the notions of inverse limit and product used in various parts of mathematics . The dual notion, colimit , generalizes direct limits and direct sums . Limits and colimits are defined via universal properties and as such provide many examples of adjoint functors For the formal definition, consider a covariant functor F J C . A limit of F is an object L of C X L F X ) for every object X of J , such that for every morphism f X Y in J , we have F f X Y , and such that the following universal property is satisfied: If F has a limit (which it need not), then the limit is defined up to a unique isomorphism, and is denoted by lim
School On Category Theory And Applications
University of Coimbra, Portugal; 1317 July 1999.Category Science Math Algebra category theory Events Past EventsSCHOOL ON category theory AND APPLICATIONS. This school is being organizedby the category theory Group of the University of Coimbra.
http://www.mat.uc.pt/~scta/
CT99
Category Science Math Algebra category theory Events Past Events
http://www.mat.uc.pt/~ct99/
Ccard V2.0 - A Category Theory Card Game
The official site for this abstract mathematical card game. You can download the deck as a gzipped Category Games Card Games Special Decks Ccard What is category theory? In a way, this game is still work in progress(as learning category theory is rather a journey than a goal).
http://www.verify-it.de/sub/ccard/

Extractions: project Ccard is a card game. You can download the cards as gzipped postscript It was born in an area of distress in May 1999, kicked of by the Summer School in Semantics (at BRICS, Aarhus University, Denmark) and in particular the course about category theory there. There are some simple "rules" I made up for two or more players (but you are of course free to change them). The seven suits are organized by a increasing number of "circles" which are meant to reflect the "difficulty" of the facts within. The number of circles/triangles of the suite symbol determines the rank of this suite. Every suite has nine cards. The highest card of one suit is the "aleph"_lambda (resembles a shaky N), followed by "omega", "infinity", then 11, 7, 5, 3, 2 (I like to stick with prime numbers) and finally the empty set (or "naught"). Each of 2 (or possibly more) players gets six cards, the rest is left as a pile on the table.
Basic Category Theory
Basic category theory. Jaap van Oosten. It is, in the author's view, the very minimumof category theory one needs to know if one is going to use it sensibly.
http://www.brics.aau.dk/BRICS/LS/95/1/BRICS-LS-95-1/BRICS-LS-95-1.html

Extractions: Jaap van Oosten January 1995 This course was given to advanced undergraduate and beginning Ph.D. students in the fall of 1994 in Aarhus, as part of Glynn Winskel's semantics course. It is, in the author's view, the very minimum of category theory one needs to know if one is going to use it sensibly. Nevertheless, two topics are breathed on, which may be skipped: there is a glimpse of categorical logic, and there is a treatment of the -calculus in cartesian closed categories. These are there to give the reader at least a very rough idea of how the theory ``works''. The text contains a bit over hundred exercises, varying in difficulty, which supplement the treatment and are warmly recommended. There is an elaborate index. Natural transformations (Co)cones and (co)limits A little piece of categorical logic Adjunctions Adjoint functors Expressing (co)completeness by existence of adjoints; preservation of (co)limits by adjoint functors
CoACT.html
CENTRE OF AUSTRALIAN category theory (CoACT). A major project of the Centre isthe application of higher dimensional category theory to computer science.
http://www.maths.mq.edu.au/~street/CoACT.html

Extractions: Use these links for further information CENTRE OF AUSTRALIAN CATEGORY THEORY (CoACT) A Macquarie University Research Centre PROFILE Director: Professor Ross Street PhD, FAustMS, FAA Professor of Mathematics Mathematics Department , Macquarie University Associate Director: Professor Michael Johnson PhD Director of the Macquarie ICT Innovations Centre Division of ICS , Macquarie University External Advisory Board Members: Professor G. Max Kelly PhD, FAA Professorial Fellow and Emeritus Professor School of Mathematics and Statistics , University of Sydney Dr Wesley Phoa BSc ANU, PhD Cambridge Capital Strategy Research The Capital Group Companies , Los Angeles Honorary Consultant Associate Professor Dominic Verity PhD Cambridge Postgraduate Coursework Programs Director Division of ICS , Macquarie University (Previously Director of Categorical Solutions General Description of the Area: Categories concern transformation and composition in mathematics. They provide an algebra of wide-spread applicability for the synthesis and analysis of systems and processes in fields as diverse as physics and computer science, but also in mathematics itself. They can be used to clarify and simplify the learning, teaching and development of mathematics. The aim of the Centre is basic research on categories, training of high quality mathematics and computer science students, and application to geometry, physics, computing, finance, and other industries.
Category Theory -- From MathWorld
Eric's other sites. Foundations of Mathematics , category theory v. CategoryTheory, The objects studied in category theory are called categories. Category.
http://mathworld.wolfram.com/CategoryTheory.html

Extractions: The branch of mathematics which formalizes a number of algebraic properties of collections of transformations between mathematical objects (such as binary relations, groups, sets, topological spaces, etc.) of the same type, subject to the constraint that the collections contain the identity mapping and are closed with respect to compositions of mappings. The objects studied in category theory are called categories Category
Category Theory Authors/titles Recent Submissions
category theory. Authors and titles for recent submissions.
http://arxiv.org/list/math.CT/recent
Category Theory Authors/titles Dec 2002
category theory. Authors and titles for Dec 2002. Higgins Comments3 pages. Latex2E Subjclass Algebraic Topology; category theory
http://arxiv.org/list/math.CT/0212
Part III Category Theory
Part III category theory. This is the main page for the Part III CategoryTheory course given in Cambridge in the academic year 20002001.
http://www.dpmms.cam.ac.uk/~leinster/categories/

Extractions: This is the main page for the Part III Category Theory course given in Cambridge in the academic year 2000-2001. All the documents produced for the course were placed here, and all of them apart from the synopsis are in the PostScript (.ps) format. Here is the lecture synopsis and recommended reading list. Here is an informal introduction to Category Theory (10 pages). The first two-thirds of this is a set of notes from the very first lecture. What's the Yoneda Lemma all about? (9 pages) A few more applications of the General Adjoint Functor Theorem , to add to the one given in lectures (one page). Section E2: The Special Adjoint Functor Theorem (7 pages, examinable!). Section F4: The Monadicity Theorem (10 pages, also examinable). Problem sheets: Sheet 1 Sheet 2 Sheet 3 (limits) Sheet 4 Here is a sheet telling you roughly what background mathematical knowledge I'm going to assume you have when I'm setting the exam. Here is a list of known mistakes in the lecture notes and problem sheets, last updated 9 December 2000. Please
Category Theory Seminar Mich 02
DPMMS Research category theory Seminar Mich 02. category theory Seminarsfor Michaelmas Term 2002. Archive of category theory Seminars
http://www.dpmms.cam.ac.uk/Seminars/Category/
CT2000
Villa Olmo, Como, Italy; 1622 July 2000.Category Science Math Algebra category theory Events Past EventsCT2000. International category theory Conference. Villa Olmo, Como, July 1622, 2000.If you see this, it probably means that your browser does not handle frames.
http://www.disi.unige.it/conferences/ct2000/

Extractions: International Category Theory Conference If you see this, it probably means that your browser does not handle frames. Follow the link to Detailed Information or that to the map of the site . Clicking buttons from there on may open pages in new windows, else remember to use your Back button to return to that page.
Category Theory And Aldor
category theory in Aldor. The idea is to begin a library of Aldor categoriesand domains organized around category theory in the mathematical sense.
http://physics.bu.edu/~youssef/aldor/aldor.html

Extractions: The idea is to begin a library of Aldor categories and domains organized around category theory in the mathematical sense. In more detail, the goals are to a) find working design patterns for categories, functors, natural transformations, adjoints within Aldor b) encode known facts about category theory (the adjoint functor theorem, for example) into the system c) produce a library implementing the most basic and useful categories. Here's a recent talk and the draft of a paper Saul Youssef
The Math Forum - Math Library - Cat. Theory/Homolgcl Alg.
sites and Web pages relating to the study of mathematics. This pagecontains sites relating to category theory/Homological Algebra.
http://mathforum.org/library/topics/category_theory/

Extractions: A short article designed to provide an introduction to category theory, a comparatively new field of mathematics that provides a universal framework for discussing fields of algebra and geometry. While the general theory and certain types of categories have attracted considerable interest, the area of homological algebra has proved most fruitful in areas of ring theory, group theory, and algebraic topology. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>
About "Applied And Computational Category Theory At RISC-Linz"
Applied and Computational category theory at RISCLinz. Library Home Full Table of Contents Suggest a Link Library Help
http://mathforum.org/library/view/12862.html

Extractions: Visit this site: http://www.risc.uni-linz.ac.at/research/category/risc/ Author: Description: Researchers; research topics; publications; events; e-mails from the Category Theory mailing list maintained and moderated by Bob Roseburgh, sorted by subject; positions announcements disseminated through the Category Theory mailing list; relevant links. For a general history and description of the research area, see Applied and Computational Category Theory. Levels: Research Languages: English Resource Types: Research Centers Math Topics: Algebraic Topology
Category Theory Reference
category theory Reference. MetaCat. The metacategory of all categories.Image map; Postscript. (Generated by dot .). Index. Abcategory;
http://www.maths.qmul.ac.uk/~mh/categories/
Graphical Database For Category Theory
Introduction; Download; Documentation; Bug Report; Contact Us. GDCTVersion 1.1 Webpage Page Modified by Matthew Graves June 27, 2002.
http://mathcs.mta.ca/research/rosebrugh/gdct/
Lars Birkedal / Teaching / Category Theory --- Fall 2000
category theory Fall 2000. A number of applications of category theory to computerscience will also be covered, including some recent developments.
http://www.itu.dk/~birkedal/teaching/category-theory-Fall-2000/

Extractions: Fall 2000 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 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. A number of applications of category theory to computer science will also be covered, including some recent developments. Lectures Tuesdays, Glentevej, Room 1.03, 9:00 AM - 12:00 AM, 2:00 PM - 4 PM

21-40 of 100 Back | 1 | 2 | 3 | 4 | 5 | Next 20