21. Category Theory And Computer Science Eugenio Moggi, Giuseppe Rosolini (Eds.) category theory and Computer Science, 7th International Conference, CTCS 97, Santa Margherita Ligure, Italy, http://www.informatik.uni-trier.de/~ley/db/conf/ctcs/index.html

Category Theory and Computer Science 10. CTCS 2004: Denmark 9. CTCS 2002: University of Ottawa, Canada Proceedings: ENTCS 69 CTCS 2002 Home Page 8. CTCS 1999: Edinburgh, Scotland, UK CTCS 1999 Home Page 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 BibTeX 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 BibTeX 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

22. Structuralism, Category Theory And Philosophy Of Mathematics While category theory has been promoted as an alternative to set theory as a foundations for mathematics, it can also be considered compatible with, http://www.mmsysgrp.com/strctcat.htm

Structuralism, Category Theory and Philosophy of Mathematics by Richard Stefanik (Washington: MSG Press,1994) Bibliography Bell,J.L."Category Theory and the Foundations of Mathematics", British Journal of Philosophy of Science , vol.32, 1981. Bell, J.L. Toposes and Local Set Theory , Clarendon Press, Oxford, 1988. Benaceraf, Paul."What Numbers Could Not Be", Philosophical review ,vol.74, 1965 Chihara, Charles. Constructibility and Mathematical Existence ,Clarendon Press, Oxford, 1990. Corry, Leo."Nicholas Bourbaki and the Concept of Mathematical Structure", Synthese ,vol.92,1992 Goldblatt, Robert. Topoi, A Categorial Analysis of Logic , North Holland, New York, 1984 Harman, Gilbert."Identifying Numbers", Analysis Jubien, Michael."Ontology and Mathematical Truth", Nous , vol.11, 1977 Katzner, Donald. Analysis Without Measurement , Cambridge University Press, Cambridge,1974 MacLane, Saunders. Mathematics: Form and Function , Springer-Verlag, new York, 1986 Resnik, Michael."Mathematics as a Science of Patterns: Ontology and Reference", Nous , vol.15, 1981

23. Category Theory For The Java Programmer « Reperiendi There are several good introductions to category theory, each written for a different audience. However, I have never seen one aimed at someone trained as a http://reperiendi.wordpress.com/2007/11/03/category-theory-for-the-java-programm

var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); reperiendi Figure it out Cartesian categories and the problem of evil The continuation passing transform and the Yoneda embedding Category Theory for the Java Programmer There are several good introductions to category theory, each written for a different audience. However, I have never seen one aimed at someone trained as a programmer rather than as a computer scientist or as a mathematician. There are programming languages that have been designed with category theory in mind, such as Haskell, OCaml, and others; however, they are not typically taught in undergraduate programming courses. Java, on the other hand, is often used as an introductory language; while it was not designed with category theory in mind, there is a lot of category theory that passes over directly. A collection of Java interfaces is the free cartesian category with equalizers on the interface objects and the built-in objects.

24. CT 2006 The International category theory Conference (CT) covers all areas of pure and applied category theory. Topics of interest include, but are not limited to http://www.mscs.dal.ca/~selinger/ct2006/

International Category Theory Conference CT 2006 White Point, Nova Scotia, June 25 - July 1, 2006 The International Category Theory Conference (CT) covers all areas of pure and applied category theory. Topics of interest include, but are not limited to: higher dimensional categories, categorical logic, applications of categories in algebra, topology, combinatorics, and other areas of mathematics, applications of category theory to computer science, physics and other mathematical sciences. Previous meetings in this series were held in Vancouver Como Coimbra Vancouver ... Halifax (1995), Tours (1994), Isle of Thorns (1992), Montreal (1991), and Como (1990). CT 2006 was held at the White Point Beach Resort in Nova Scotia (Canada). It was an active research-oriented conference, in something of an "Oberwolfach style". The seaside setting offered more opportunities for informal discussion and collaboration in the evenings than might have been the case in an urban setting. There were also many opportunities for recreational activities. All those interested in category theory and its applications were welcome.

25. Good Math, Bad Math This is one of the last posts in my series on category theory; category theory provides a good framework for defining linear logic and for building a http://scienceblogs.com/goodmath/goodmath/category_theory/

@import url(/seed-static/global.css); @import url(/seed-static/NEWNEW.css); @import url(http://www.seedmagazine.com/seed-static/inc/masthead.css); Seed Media Group document.write(''); Latest Posts Archives About RSS ... Contact Search this blog Profile Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems. Other Information Recent Posts Vox Day on Women in Science Science Diversity Meme: The CS Mutant Meta out the wazoo: Monads and Monoids Dazzling Egnorance: Egnor vs. Experimental Science ... Responding to Granville Sewell about his Fraudulent Experiments Recent Comments Nomen Nescio on Vox Day on Women in Science Mark C. Chu-Carroll on Vox Day on Women in Science MikeT on Vox Day on Women in Science free music on Categories: Products, Exponentials, and the Cartesian Closed Categories Julie Stahlhut on Vox Day on Women in Science rimpal on Vox Day on Women in Science Leigh on Vox Day on Women in Science MiddleAgeMan on Vox Day on Women in Science MiddleAgeMan on Vox Day on Women in Science trrll on Dazzling Egnorance: Egnor vs. Experimental Science

26. Understanding Category Theory And Its Practical Applications | Lambda The Ultima However, I have not been able to identify any such gains from category theory. I can t see how it is any better than anything else. http://lambda-the-ultimate.org/node/2604

@import "misc/drupal.css"; @import "themes/chameleon/ltu/style.css"; Lambda the Ultimate Home Feedback FAQ ... Archives User login Username: Password: Create new account Request new password Navigation recent posts Home forums LtU Forum Understanding category theory and its practical applications Note on the obvious: these thoughts represent my original state of mind when this post was first made, and do not necessarily reflect my current understanding. This OP is left unmodified for reference purposes. Introduction Various logics and mathematics, such as set theory, predicate calculus, arithmetic, et. al. were relatively intuitive and came easy to grasp when I learned them. Additionally, they came with their obvious applications, not just to problems in the real world, but also to programming and programming languages. It is easy to see the higher level of abstraction that comes from using these as opposed to a computation-oriented programming language. Predicate calculus, in particular, is a powerful language suited to various boons from a programmer's perspective, including arbitrary constraint qualification as a means to better aspect-oriented programming. However, I have not been able to identify any such gains from category theory. I can't see how it is any better than anything else. Note: My understanding of category theory is very shoddy, so using lots of category-theoretic terminology may obscure my understanding of your answerbeing moderate will help. From what I gather, a morphism seems to be a transformation (possibly represented by one or more functions), and the objects in a category could be represented as a set. But if I am right, then how is category theory any better than just simply using functions, relations, and set theory?

27. CTCS'04 CTCS 04 is the tenth conference on category theory and Computer Science. The purpose of this conference series is the advancement of the foundations of http://www.itu.dk/research/theory/ctcs2004/

Category Theory and Computer Science (CTCS'04) August 12th-14th, 2004 Appsem II conference DEADLINE EXTENSION: April 16th (closed) FIRST Graduate Student Summer School, August 9th-11th, 2004 Workshop on Categorical Methods in Concurrency, Interaction and Mobility (CMCIM), August 11th, 2004 The IT University of Copenhagen. Illustration by Eyecadcher. CTCS'04 is the tenth conference on Category Theory and Computer Science. The purpose of this conference series is the advancement of the foundations of computing, using the tools of category theory. While the emphasis is on applications of category theory, it is recognized that the area is highly interdisciplinary. Category theory, after having played a major role in the development of mathematics, e.g. in algebraic geometry, has been widely applied by logicians to obtain concise interpretations of many logical concepts. On the other hand, links between logic and computer science have been developed now for over twenty years, notably via the Curry-Howard isomorphism, which identifies programs with proofs. Together, the triangle category theory-logic-computation presents a rich world of interconnections. It is the primary purpose of the CTCS conference series to explore these interconnections. Conference proceedings will appear in Electronic Notes in Theoretical Computer Science . Paper copies of the proceedings will be available to participants at the conference.

28. Comcat www.unico.it/~walters/comcat/comcatproj.html Similar pages CT2007 - Home PageCT2007 is an international conference devoted to category theory. The meeting is being organized by the category theory Group of the University of http://www.unico.it/~walters/comcat/comcatproj.html

The Computational Category Theory Project 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. (There is a related Categorical Computation Project concerned with a categorical analysis of computers, computation and programming.) The groups currently connected with this project are: Contact R.F.C. Walters, walters@fis.unico.it Mt. Allison University, Sackville, New Brunswick, Canada Contact Bob Rosebrugh, rrosebrugh@mta.ca School of Mathematics, University of Wales, Bangor, Wales Contact Ronnie Brown Computing Department, Macquarie University, Sydney, Australia Contact Mike Johnson MCS, University of Leicester, England Contact Anne Heyworth The organization of the project is as follows: Each group in the project will maintain a home page on the web with details of its own work and with links to the other groups. 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. New versions will be announced on the Categories Mailing List.

29. Old Science, New Science At Freedom Of Science Only category theory I know I learned it from this article. And that was a while back. I have to read it again carefully. Can you explain why you say that? http://globalpioneering.com/wp02/old-science-new-science/

Freedom of Science Transfer scientific authority to people Home Freedom of Science About Contact ... Old science, new science Published by November 14th, 2007 in Science Physics Newton Standards If Newton were alive today he would not be doing physics, he would be busy contributing to the new science of networks. properties of networks This is the same idea, a physicist, Lee Smolin , investigates in Chapter 4 of Three Roads to Quantum Gravity. academic categories will help. What do you think? To Newton, Christian-Peripatetic mixture taught as science in Cambridge looked like Occult-Newtonian mixture taught as science today. Both are ossified scholastic systems. [ Future now ShareThis Feed for this Entry Trackback Address ... Nov 14th, 2007 at 8:54 pm Only category theory I know I learned it from this article. And that was a while back. I have to read it again carefully. Can you explain why you say that? Carl Brannen Nov 14th, 2007 at 11:03 pm Nov 18th, 2007 at 8:35 pm So, when I notice that both a computer scientist and a physicist describe the world as connections am I doing category theory? Posting Your Comment Please Wait Leave a Reply There was an error with your comment, please try again.

30. Category Theory And Applications category theory is a mathematical discipline that is characterized by its role in unifying mathematics as well as its foundational vocation. http://www.math.uqam.ca/ism/index_en.html?regroupements/categorie_en.shtml

31. Basic Concepts Of Enriched Category Theory Basic Concepts of Enriched category theory. G.M. Kelly. Originally published as Cambridge University Press, Lecture Notes in Mathematics 64, 1982. http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html

Basic Concepts of Enriched Category Theory G.M. Kelly Originally published as: Cambridge University Press, Lecture Notes in Mathematics 64, 1982. Keywords: enriched categories, monoidal categories 2000 MSC: 18-02, 18D10, 18D20 Republished in: Reprints in Theory and Applications of Categories , No. 10 (2005) pp. 1-136 http://www.tac.mta.ca/tac/reprints/articles/10/tr10.dvi http://www.tac.mta.ca/tac/reprints/articles/10/tr10.ps http://www.tac.mta.ca/tac/reprints/articles/10/tr10.pdf TAC Reprints Home

32. Courses: Barr / Wells An introduction to category theory Categories, functors and natural Barr Wells, category theory Lecture Notes for ESSLLI (Postscript Document) http://www.let.uu.nl/esslli/Courses/barr-wells.html

Home Overview News Related Events Program Timetable Courses and Workshops Student Session Evening Lectures Registration Check In Registration Procedure Accommodation Registration Form Local Information Local Team Lecturers Social Program Order and Enlist ... Local Guide Sponsors Sponsors Industrial Programme I NTRODUCTION TO C ATEGORY T HEORY B ARR and W ELLS C OURSE D ESCRIPTION An introduction to category theory: Categories, functors and natural transformations. Limits and colimits. Adjoint functors. Triples and Kleisli categories. Cartesian closed categories, toposes, and related categories. Categories with monoidal structure; *-autonomous categories. L ITERATURE Category Theory Lecture Notes for ESSLLI Postscript Document Categories for Computing Science P REREQUISITES Some previous work with mathematical structures defined by axioms, such as monoids, groups, or lattices, and familiarity with abstract mathematical reasoning.

33. Category Theory (mathematics) -- Britannica Online Encyclopedia major reference, history of algebra, work of Mac Lane. http://www.britannica.com/eb/topic-99404/category-theory

Already a member? LOGIN Encyclopædia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to this Topic Shopping New! Britannica Book of the Year The Ultimate Review of 2007. 2007 Britannica Encyclopedia Set (32-Volume Set) Revised, updated, and still unrivaled. New! Britannica 2008 Ultimate DVD/CD-ROM The world's premier software reference source. category theory (mathematics) A selection of articles discussing this topic. major reference Category theory history of algebra 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... work of Mac Lane ...Samuel Eilenberg noticed that they applied to the topology of infinitely coiled curves called solenoids. To understand and generalize this link between algebra and topology, the two men created category theory, the general cohomology of groups, and the basis for the Eilenberg-Steenrod axioms for homology of topological spaces. Mac Lane worked with categorical duality and defined categorical... No results were returned.

34. Ars Mathematica » Blog Archive » Opinions Of Category Theory I am a big fan of category theory, and have used it in some published papers. But I do not believe that it is saviour (sorry, that’s how I spell that word) http://www.arsmathematica.net/archives/2006/06/24/opinions-of-category-theory/

Ars Mathematica Dedicated to the mathematical arts. June/July Notices Releasing LHC Data Opinions of Category Theory June 24th, 2006 by Walt Is category theory the savior of mathematics, or its destroyer? Discuss. This entry was posted on Saturday, June 24th, 2006 at 8:29 pm and is filed under Mathematics . You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response , or trackback from your own site. JacquesC Says: June 25th, 2006 at 7:03 pm Is the fact that this entry is filed under Uncategorized a not-so-subtle hint of the opinion of the poster? just another tool. It is particularly useful when one wants to expose structure ; it can be just as bad a tool, say when one is doing pure computations. I use category theory, I use set theory, I use various logics, I use type theory, whatever the best tool for the job at hand. PeterMcB Says: June 26th, 2006 at 2:30 am For me, however, there is another role which is just as valuable: CT provides a framework to describe the doing of mathematics itself. This is neat! Walt Says: June 26th, 2006 at 10:29 am

35. 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 postscript. http://www.verify-it.de/sub/ccard/index.html

This page is part of the Mozilla Open Directory project Ccard 2.0 or: How to make fun out of something highly abstract. Ccard is a card game. You can download the cards as gzipped postscript here (to be printed 2-sided) or here (single sided) with extra backside 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. How to play? 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.

36. PlanetMath Category Theory As a tool, category theory allows mathematicians to focus on the morphisms between objects rather than their elements. In many cases, these morphisms are http://planetmath.org/encyclopedia/CategoryTheory.html

37. Category Theory And The Category Of Haskell Programs : Part 1 category theory is an expression that is generally frightening people. But, if you have attempted to read some research papers in Computer Science, http://www.alpheccar.org/en/posts/show/74

Category Theory and the category of Haskell programs : Part 1 Posted by alpheccar - Jun 18 2007 at 22:59 CEST "Category theory" is an expression that is generally frightening people. But, if you have attempted to read some research papers in Computer Science, Mathematics, Physics or even Philosophy, you've surely remarked that Category theory is used a lot and you probably asked yourself : what is Category theory ? Why is it so useful ? Is it so difficult ? What the link(s) with computer science ? Answering to those questions in an easy way that can be understood by most people is really challenging but I am going to try and I'll use the category of Haskell programs to illustrate some points. I hope the experts will forgive me some slight inaccuracies and/or an unconventional presentation. What is a category ? Category theory is used a lot because it is a theory of processes in the most general meaning of the word. Indeed, what do all processes have in common ? Answer : they can be composed and the composition is associative. So, a category is just a bunch of objects A,B,C ... and some processes f,g,h ... I'll note a process f applied to A to get B with an Haskell syntax: f A B A is the domain of f and B the codomain. It is wrong to say that the image of f is included in B. f is not a function.

38. Category Theory Research Of Victor Porton - Pure Category Theory + category theory pages on this site Original fundamental abstract math theories by Victor Porton. http://www.mathematics21.org/category-theory.html

39. Haskell/Category Theory - Wikibooks, Collection Of Open-content Textbooks This article attempts to give an overview of category theory, insofar as it applies to Haskell. To this end, Haskell code will be given alongside the http://en.wikibooks.org/wiki/Haskell/Category_theory

Haskell/Category theory From Wikibooks, the open-content textbooks collection Haskell Jump to: navigation search Category theory Solutions Contents Introduction to categories Category laws Hask, the Haskell category Functors ... Notes Wider Theory Denotational semantics Equational reasoning Program derivation Category theory The Curry-Howard isomorphism edit this chapter This article attempts to give an overview of category theory, insofar as it applies to Haskell. To this end, Haskell code will be given alongside the mathematical definitions. Absolute rigour is not followed; in its place, we seek to give the reader an intuitive feel for what the concepts of category theory are and how they relate to Haskell. edit Introduction to categories A simple category, with three objects A B and C , three identity morphisms i d A i d B and i d C , and two other morphisms and . The third element (the specification of how to compose the morphisms) is not shown. A category is, in essence, a simple collection. It has three components: A collection of objects A collection of morphisms , each of which ties two objects (a source object and a target object ) together. (These are sometimes called

40. Category Theory - HaskellWiki category theory can be helpful in understanding Haskell s type system. There exists a Haskell category , of which the objects are Haskell types, http://www.haskell.org/haskellwiki/Category_theory

Haskell Wiki community Recent changes Random page ... Special pages Not logged in Log in Help Edit this page Discuss this page ... Related changes Category theory Categories Theoretical foundations Mathematics Haskell theoretical foundations General Mathematics Category theory Research Curry/Howard/Lambek Lambda calculus Alpha conversion ... Lambda abstraction Other Recursion Combinatory logic Chaitin's construction Turing machine ... Relational algebra Category theory can be helpful in understanding Haskell's type system. There exists a "Haskell category", of which the objects are Haskell types, and the morphisms from types a to b are Haskell functions of type a b . Various other Haskell structures can be used to make it a Cartesian closed category. Contents Defintion of a category Axioms Examples of categories Further definitions ... See also The Haskell wikibooks has an introduction to Category theory , written specifically with Haskell programmers in mind. edit 1 Defintion of a category A category consists of two collections: Ob , the objects of Ar , the arrows of (which are not the same as Arrows defined in GHC Each arrow f in Ar has a domain, dom

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