41. 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 2004 Course Information Place: PH 225B Time: TR 3 - 4:20 Instructor: Steve Awodey Office: Baker 152 (mail: Baker 135) Office Hour: Monday 4 - 5, or by appointment Phone: x8947 Email: awodey@andrew Secretary: Baker 135 TA: Michael Warren Office Hour: Tuesday 4:30 - 5:30, BH 143 Webpage: www.andrew.cmu.edu/course/80-413-713 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.

42. Gian Luca Cattani's Home Page University of Cambridge Applications of category theory to computer science, semantics of concurrent process languages. http://www.cl.cam.ac.uk/users/glc25/

NOTICE I am currently working for DS Data Systems . This is a snapshot of my web-page as it was when I left Cambridge and it is still available mainly to allow people to have access to my research papers. The Computer Science Department at Aarhus is warmly thanked for hosting this page. In fact I also still receive emails sent to either my Aarhus or Cambridge addresses. November 2000 Gian Luca Cattani I am a Research Associate at Cambridge University Computer Laboratory and a Fellow of Wolfson College . I did my doctorate at BRICS under the supervision of Glynn Winskel Research My main research interests are in Logics and Semantics of Computation. In particular Models of Concurrent Computation and applications of Category Theory to Computer Science especially in connection with Domain Theory, Denotational and Operational Semantics. Presently I am supported by an EPSRC grant, whose title is `Calculi for Interactive Systems: Theory and Experiment' and whose principal investigator is Robin Milner. On-line papers and a bibtex database of my publications.

43. Category Theory -- From MathWorld category theory. The branch mappings. The objects studied in category theory are called categories. Category. search. Eric W. Weisstein. Category http://mathworld.wolfram.com/CategoryTheory.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Category Theory Category Theory 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 search Eric W. Weisstein. "Category Theory." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/CategoryTheory.html Wolfram Research, Inc.

44. Mathematical Structures Group Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science. Bibliographic data. http://www.mmsysgrp.com/mathstrc.htm

MATHEMATICAL STRUCTURES Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science. Research Bibliography Mathematical Theories and Models Scientific Theories and Models Category Theory Theoretical Computer Science ... WWW Research Sites Mathematical Theories and Models Agazzi and Darvas. Philosophy of Mathematics Today. Kluwer Academic Publishers, 1997 Anglin and Lambek. The Heritage of Thales. Springer-Verlag, 1995 Akin, Ethan. The General Topology of Dynamical Systems. American Mathematical Society, 1993 Barwise, Jon. (ed) Handbook of Mathematical Logic. North-Holland,1977 Barwise, Jon. "Axioms for Abstract Model Theory" ,Annals of Mathematical Logic 7(1974) 221-265. Bell, John and Machover,Moshe. A Course in Mathematical Logic. North-Holland, 1977 Bridge, Jane. Beginning Model Theory. Clarendon Press, 1977 Burgess, John and Rosen, Gifeon. A Subject with No Object Oxford Press, 1997

45. Category Theory Authors/titles Recent Submissions category theory. Title Cofree coalgebras over operads II Authors Justin R. Smith Subjclass Algebraic Topology; category theory MSC-class 18D50, 55P15 http://arxiv.org/list/math.CT/recent

Category Theory Authors and titles for recent submissions Fri, 4 Jun 2004 Thu, 3 Jun 2004 Fri, 28 May 2004 Tue, 25 May 2004 ... Thu, 13 May 2004 Fri, 4 Jun 2004 math.CT/0406061 abs ps pdf other Title: Tours de torseurs, geometrie differentielle des suites de fibres principaux, et theorie des cordes Authors: Aristide Tsemo Subj-class: Category Theory Thu, 3 Jun 2004 math.GR/0406044 abs ps pdf other Title: On the Zappa-Szep Product Authors: Matthew G. Brin Comments: 29 pages Subj-class: Group Theory; Category Theory MSC-class: Fri, 28 May 2004 math.QA/0405517 abs ps pdf other Title: Fiber Functors on Temperley-Lieb Categories Authors: Yamagami Shigeru Comments: 19 pages Subj-class: Quantum Algebra; Category Theory Tue, 25 May 2004 math.AG/0405453 abs ps pdf other Title: Authors: Michel Hickel Comments: 45 pages, french Subj-class: Algebraic Geometry; Category Theory MSC-class: Thu, 13 May 2004 math.KT/0405227 abs ps pdf other Title: Hochschild cohomology of abelian categories and ringed spaces Authors: W. T. Lowen M. Van den Bergh Comments: 38 pages Subj-class: K-Theory and Homology; Category Theory

46. Lars Birkedal / Teaching / Category Theory --- Fall 2000 category theory Fall 2000. A number of applications of category theory to computer science will also be covered, including some recent developments. http://www.itu.dk/~birkedal/teaching/category-theory-Fall-2000/

Category Theory Fall 2000 Instructors: Lars Birkedal birkedal@it-c.dk , Glentevej 67, Room 2.21, 3816 8868 Thomas Hildebrandt hilde@it-c.dk , Glentevej 67, Room 2.46, 3816 8833 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. Course Information Lectures Tuesdays, Glentevej, Room 1.03, 9:00 AM - 12:00 AM, 2:00 PM - 4 PM

47. Ian Stark - University Of Edinburgh University of Edinburgh Formal semantics of programming languages, category theory, domain theory and structural operational semantics, functional languages. http://www.dcs.ed.ac.uk/~stark/

Ian Stark Lecturer in Computer Science Laboratory for Foundations of Computer Science School of Informatics The University of Edinburgh Edinburgh EH9 3JZ Scotland Photograph Email: Ian.Stark@ed.ac.uk Phone: +44 (131) 650 5143 (Work) +44 (131) 228 4101 (Home) Fax: Office: JCMB 2506 Research Other pages list my publications and some talks EPSRC Advanced Research Fellowship on Mathematical Models for Concurrent and Mobile Computation . I am also involved with the following research projects: Mobile Resource Guarantees Edinburgh .NET lab Reasoning with Names and Identity in Programming Languages APPSEM II : European network for Applied Semantics MLj : A compiler for Standard ML which produces Java bytecodes PhD students: Uli Schöpp Sam Lindley Tom Chothia (completed 2002) I am second supervisor for Rob Atkey Jonathan Cook Shin-Ya Katsumata Alex Blewitt and Francis Tang completed 2002 Teaching I'm not giving any undergraduate lecture courses for the duration of my EPSRC research fellowship. Here are some past courses. Advanced Programming in Java Language Processing Computer Literacy: Algorithms and Programs.

48. CTCS'04 category theory and Computer Science (CTCS 04) August 12th14th, 2004 Appsem II conference. DEADLINE EXTENSION April 16th (closed). 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.

49. Kosta Dosen's Home Page University of Belgrade Proof theory, category theory. http://www.mi.sanu.ac.yu/~kosta/

Kosta Došen Mathematical Institute SANU Kneza Mihaila 35, Belgrade, Yugoslavia Tel.: (381-11) 630-170 (381-11) 180-591 Fax.: (381-11) 186-105 E-MAIL: kosta@mi.sanu.ac.yu Curriculum Vitae Research Interest Publications Curriculum Vitae Born : 5 June 1954 in Belgrade, Yugoslavia. Education : University of Belgrade, University of Oxford. Doctoral thesis : Logical Constants: An Essay in Proof Theory, Oxford, 1980. Tenured posts Mathematical Institute, Belgrade (since 1981, full professor since 1995), Institut de Recherche en Informatique de Toulouse, Department of Mathematics and Computer Science, University of Toulouse III (professor since 1994). Faculty of Philosophy, University of Belgrade (full professor since 2003). Visiting posts Faculty of Mathematics, University of Belgrade, (1985/86, 1990-92, 2001), University of Notre Dame, Indiana (1986/87), Institute of Mathematics, University of Montenegro (1988/89), Department of Mathematics and Computer Science, University of Montpellier III (1992-94), Wilhelm Schickard Institute, University of Tübingen (1997).

50. CT2000 CT2000. 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/

International Category Theory Conference Villa Olmo, Como, July 16-22, 2000 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.

51. CTO : Category Theory 101 category theory 101. A Learning Lounge course about category theory. Short introduction category theory entry on the Stanford Encyclopedia of Philosophy. http://cliki.tunes.org/Category Theory 101

CTO CLiki for the TUNES project Home Recent Changes About CLiki Text Formatting ... Create New Page Category Theory 101 A Learning Lounge course about Category Theory The basics: A category is a thing with objects and arrows (called morphism s) that lead between the objects. The arrows have heads and tails. They are abstract in the sense that they can represent anything with complex structure or even no structure at all. Many categories are different, and there are types of categories. All categories follow some basic rules. The differences otherwise can be enormous, though: For every object there is an identity arrow over that object that just leads from that object to that object. There may be other identities over that object, but one is distinctly the identity If one arrow leads to an object from which another arrow leads, then those arrows can compose. All such arrows compose, but what you can say about the resulting arrow differs from category to category. Some arrows are the reverse or inverse of others. There are some basic examples of categories: one is Set, whose objects are sets and whose arrows are (total) functions between sets. The category Set's natural composition is therefore function composition.

52. CTO : Category Theory category theory. See our category theory 101 overview. category theory is very useful in formalizing types and functions/functors in functional programming. http://cliki.tunes.org/Category Theory

CTO CLiki for the TUNES project Home Recent Changes About CLiki Text Formatting ... Create New Page Category Theory The term for a very abstract (often too abstract for most) theory in mathematics relating several fields through some common properties. See our Category Theory 101 overview. Category theory is very useful in formalizing types and functions/functors in functional programming. Pages in this topic: Category Theory 101 Morphism Also linked from: Aldor Algebra and coalgebra Bisimulation Charity ... View source

53. Ramifications Of Category Theory Workshop And Symposium Including Ramifications of category theory Workshop and Symposium Including a lecture series by FW Lawvere Sponsored by AILA (Associazione Italiana di Logica e http://ramcat.scform.unifi.it/

54. Paul Taylor Includes papers on category theory. http://www.dcs.qmw.ac.uk/~pt/

Paul Taylor Research Fellow (RA3) funded by EPSRC GR/S58522 Abstract Stone Duality Please note: My papers and web pages at www.cs.man.ac.uk/ pt are currently under reconstruction. All of the L A T E X documents are being rebuilt (which in some cases involves upgrading from L A T E X2.09 to L A T E X e ) and regenerated in DVI, PDF, PS and A4 booklet form, with hyperlinks. All of the HTML documents are being rebuilt using TTH, accompanied by DVI and PDF versions. This will allow you to use XDVI, XPDF or ACROREAD to navigate the system of papers entirely in DVI or PDF format, without returning to HTML The T E X macro packages are also being upgraded. For the time being, you may encounter erroneous web links. In particular, if you find yourself redirected to localhost www.localhost.com www.di.unito.it or www.dcs.qmul.ac.uk please report the bug to me and substitute www.cs.man.ac.uk or www.dcs.qmul.ac.uk My book, Practical Foundations of Mathematics , was published by Cambridge University Press in 1999, ISBN 0-521-63107-6. (This link is intentionally still to www.dcs.qmul.ac.uk

55. Week68 Goldblatt s book teaches you all the category theory you need to learn about topoi but for people who already know some category http://math.ucr.edu/home/baez/week68.html

October 29, 1995 This Week's Finds in Mathematical Physics (Week 68) John Baez Okay, now the time has come to speak of many things: of topoi, glueballs, communication between branches in the many-worlds interpretation of quantum theory, knots, and quantum gravity. 1) Robert Goldblatt, Topoi, the Categorial Analysis of Logic, Studies in logic and the foundations of mathematics vol. 98, North-Holland, New York, 1984. If you've ever been interested in logic, you've got to read this book. Unless you learn a bit about topoi, you are really missing lots of the fun. The basic idea is simple and profound: abstract the basic concepts of set theory, so as to define the notion of a "topos", a kind of universe like the world of classical logic and set theory, but far more general! For example, there are "intuitionistic" topoi in which Brouwer reigns supreme - that is, you can't do proof by contradiction, you can't use the axiom of choice, etc.. There is also the "effective topos" of Hyland in which Turing reigns supreme - for example, the only functions are the effectively computable ones. There is also a "finitary" topos in which all sets are finite. So there are topoi to satisfy various sorts of ascetic mathematicians who want a stripped-down, minimal form of mathematics. However, there are also topoi for the folks who want a mathematical universe with lots of horsepower and all the options! There are topoi in which everything is a function of time: the membership of sets, the truth-values of propositions, and so on all depend on time. There are topoi in which everything has a particular group of symmetries. Then there are *really* high-powered things like topoi of sheaves on a category equipped with a Grothendieck topology....

56. Ccard V2.0 - A Category Theory Card Game 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/

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.

57. Centre Of Australian Category Theory, Macquarie University Centre of Australian category theory. Welcome to the Centre of Australian category theory. The Centre of Australian category theory http://www.ics.mq.edu.au/CoACT/

CoACT members projects awards ... Staff Centre of Australian Category Theory Welcome to the Centre of Australian Category Theory The Centre of Australian Category Theory (CoACT) develops an algebra of widespread applicability for the synthesis and analysis of systems and processes in fields as diverse as physics and computer science, and also mathematics itself. Although having operated as a coherent group since the founding of the on-going Australian Category Seminar in 1971, CoACT was formally established in 1999. Vision To provide the environment for the top international centre for Higher-dimensional Category Theory and a major international centre for general Category Theory. Mission To pursue vigorously research into those parts of mathematics and computer science which find natural expression and advancement in terms of Category Theory and to train thehighest-quality research students. More information about CoACT can be found in the History Objectives Performance Indicators and Benchmarks and Constitution Further Information We welcome your enquiries about our work - please contact the Director Professor Ross Street Your Privacy Comments?

58. 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

59. Category Theory category theory. (This is not a category for pages about theory. Rather, the name of this page refers to the mathematical field of category theory.). http://c2.com/cgi/wiki?CategoryTheory

60. 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/

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