21. Jim Renshaw's Homepage University of Southampton. Algebraic semigroups, semigroup amalgams, automata/category theory, computer aided learning. Publications, teaching material, semigroup resources. http://www.maths.soton.ac.uk/jhr/

about us people scholarships applied group ... university pages Name Dr JH Renshaw Room Phone Email obfmessage("W-U-Erafunj+znguf-fbgba-np-hx","W-U-Erafunj+znguf-fbgba-np-hx") Research Interests Algebraic semigroups semigroup amalgams, automata/category theory, computer aided learning. Links Pure Group Recent Preprints Teaching Materials Publications List ... Semigroup Forum My Family Tree Ocean Brass . Support us by buying online at www.buy.at/oceanbrass/

22. Toposes, Triples And Theories A book by Michael Barr and Charles Wells originally published by Springer Verlag. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

23. Categories category theory is popular among algebraic topologists. John Baez and JamesDolan, Categorification, in Higher category theory, eds. http://math.ucr.edu/home/baez/categories.html

Categories, Quantization, and Much More John Baez September 26, 2004 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.

24. Steve Awodey Carnegie Mellon University category theory, logic, history and philosophy of mathematics and logic. http://www.andrew.cmu.edu/user/awodey/

Steve Awodey Associate Professor Department of Philosophy Carnegie Mellon University Research Areas: Category Theory Logic Philosophy of Mathematics History of Logic and Analytic Philosophy Connections: Algebraic Set Theory Logic of Types and Computation Selected Current Preprints Algebraic models of intuitionistic theories of sets and classes. S. Awodey and H. Forssell, July 2004. Predicative algebraic set theory S. Awodey and M. Warren, July 2004. Relating topos theory and set theory via categories of classes. S. Awodey, C. Butz, A. Simpson, T. Streicher, June 2003. Ultrasheaves and Double Negation. S. Awodey and J. Eliasson, 2002. Propositions as [types]. S. Awodey and A. Bauer, Tech. Report Institut Mittag Leffler, June 2001. Continuity and Logical Completeness [ps] [pdf]. S. Awodey, December 2000. The Coalgebraic Dual of Birkhoff's Variety Theorem. S. Awodey and J. Hughes, October 2000. Selected Publications Sheaf Toposes for Realizability. S. Awodey and A. Bauer, Archive for Mathemtical Logic , forthcoming.

25. Boston.com / News / Boston Globe / Obituaries / Saunders Mac Lane In a landmark paper he cowrote with Samuel Eilenberg in 1945, Dr. Mac Lane detailed what came to be known as the category theory. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

26. Week202 and the basic rules of category theory. It s not as efficient, After anearlier version of this Week appeared on the category theory mailing list, http://math.ucr.edu/home/baez/week202.html

February 21, 2004 This Week's Finds in Mathematical Physics (Week 202) John Baez This week I'll deviate from my plan of discussing number theory, and instead say a bit about something else that's been on my mind lately: structure types. But, you'll see my fascination with Galois theory lurking beneath the surface. Andre Joyal invented structure types in 1981 - he called them "espèces de structure", and lots of people call them "species". Basically, a structure type is just any sort of structure we can put on finite sets: an ordering, a coloring, a partition, or whatever. In combinatorics we count such structures using "generating functions". A generating function is a power series where the coefficient of x n keeps track of how many structures of the given kind we can put on an n-element set. By playing around with these functions, we can often figure out the coefficients and get explicit formulas - or at least asymptotic formulas - that count the structures in question. The reason this works is that operations on generating functions come from operations on structure types. For example, in "

27. Centre De Recherche En Th Orie Des Cat Gories Montr Al category theory Research Centre. Announcements of weekly seminars, conferences, and other research activities in category theory. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

28. Category Theory category theory, a branch of abstract algebra, has found many Like such fieldsas elementary logic and set theory, category theory provides a basic 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.

29. 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.

30. Alsani's Descent Category Theory WebPage! This page is merely a launching pad to sites of interest in Descent or category theory. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

31. The Computational Category Theory Project The aim of the project is the development of software on a wide variety of platforms for computing with mathematical categories and associated http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

32. Untitled Document Pace University. Problem decomposition and theory reformulation, integrated cognitive architectures for autonomous robots, distributed constraint satisfaction problems, semigroup theory and dynamical systems, category theory in software design. http://csis.pace.edu/~benjamin/

33. CATEGORY THEORY AT MCGILL category theory at McGill. Silvia Bunge and Carl Christian Mikkelsen, Montreal 78.category theory Category theorists are conceptual mathematicians of a http://www.math.mcgill.ca/bunge/ctatmcgill.html

Category Theory at McGill Silvia Bunge and Carl Christian Mikkelsen, Montreal '78 Category Theory Category theorists are conceptual mathematicians of a special kind. What binds them together is that they approach mathematical problems with a point of view that is radically different from that on which traditional mathematics is based, and which emphasizes interactions between mathematical objects over their individual constituents. Their results are often surprising, provide new insights, and are obtained by the invention of sophisticated notions, theories, and techniques. Category Theory is only little more than 50 years old (dating it back to the work of S. Eilenberg and S. MacLane in 1945) yet, its impact on several branches of mathematics has been considerable, in spite of the reluctance to recognize it as a revolutionary independent field dealing with foundational questions, very different from Set Theory. Category Theory at McGill The Montreal Categories Center Current Research Areas in Category Theory at McGill Three areas deserve attention because of the novelties they bring and because they are part of a truly international joint effort. Let us refer to them as "Grothendieck's Program", "Lawvere's Program", and "Computational Category Theory". Although not pairwise disjoint, their objectives are different and can be briefly described as follows.

34. Mahdavi SUNY Potsdam, NY, USA; 26 June 2003. http://www2.potsdam.edu/mahdavk/Conf.htm

Math. Dept. Registration Financial Support SUNY Potsdam ... Map of Parking Lots Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics. SUNY Potsdam June 2-6, 2003 Speakers S CHEDULES ABSTRACTS This workshop investigates the interactions between Representation Theories, Knot Theory, Topology, quantum Field Theory, Category Theory, and Mathematical Physics. This conference will be of great benefit to the researchers, recent Ph.Ds, and graduate students. Some financial support is available for graduate students, recent Ph.Ds, and others who are qualified. REGISTRATION Total cost of room and board, on Campus, is $206.50 Participants who choose to stay on campus will be housed in Draime Hall SUNY Potsdam Map) Off Campus housing Hotel listing (you need to make your own reservation) a block of rooms has been reserved at Clarkson Inn. For reservation please call 1 800 790 6970, before May 15, 2003($89.00 for single, and$99.00 for double, per night). you need to mention SUNY Potsdam math. conference.

35. Www.risc.uni-linz.ac.at/research/category/ www.risc.unilinz.ac.at/research/category/risc/ CTO category theory 101category theory entry on the Stanford Encyclopedia of Philosophy. category theoryentry on Eric Weisstein s World of Mathematics by Eric W. Weisstein. http://www.risc.uni-linz.ac.at/research/category/

36. 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.

37. CTO : Category Theory category theory. The term for a very abstract (often too abstract for most) See our category theory 101 overview. category theory is very useful in 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

38. Martin Hofmann's Home Page University of Edinburgh Type theory, principles of programming languages, semantics, category theory, mathematical logic, formal methods. http://www.dcs.ed.ac.uk/~mxh/

Martin Hofmann I have moved to Munich. Please visit my new homepage

39. Pitts, Andrew University of Cambridge Applications of mathematical logic and category theory to computer science, semantics of programming languages and type theories, formal logics for reasoning about program properties. http://www.cl.cam.ac.uk/users/amp12/

Andrew Pitts Picture Professor of Theoretical Computer Science Fellow of Darwin College Research interests I am interested in all aspects of programming language semantics, be they operational or denotational (or somewhere between the two). I try to use various tools from mathematical logic and category theory to advance the foundations of programming language semantics. I am also interested in type theories, formal logics for reasoning about program properties, and the design and implementation of metaprogramming languages. Publications: listing BibTeX database Recent talks The FreshML research project. APPSEM II thematic network funded by the IST programme of the European Union. I participate in the Cambridge Theory and Semantics Group Journals I am associated with: Applied Categorical Structures Chicago Journal of Theoretical Computer Science Higher-Order and Symbolic Computation Mathematical Structures in Computer Science Upcoming events: 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005) , Oxford, UK, 22-25 August 2005. [Invited speaker] International Summer School On Applied Semantics (APPSEM II 2005) , Frauenchiemsee, Germany, 8-12 September 2005. [Lecturer]

40. Category Theory category theory is a general mathematical theory of structures and sytems of One of the interesting features of category theory is that it provides a http://setis.library.usyd.edu.au/stanford/archives/fall1997/entries/category-the

This is a file in the archives of the Stanford Encyclopedia of Philosophy Stanford Encyclopedia of Philosophy A B C D ... Z Category Theory Category theory is a general mathematical theory of structures and sytems of structures. It allows us to see, among other things, how structures of different kinds are related to one another as well as the universal components of a family of structures of a given kind. The theory is philosophically relevant in more than one way. For one thing, it is considered by many as being an alternative to set theory as a foundation for mathematics. Furthermore, it can be thought of as constituting a theory of concepts. Finally, it sheds a new light on many traditional philosophical questions, for instance on the nature of reference and truth. General Definitions Brief Historical Sketch Philosophical Significance Bibliography ... Related Entries General Definitions Category theory is a generalized mathematical theory of structures. One of its goals is to reveal the universal properties of structures of a given kind via their relationships with one another. Formally, a category C can be described as a collection Ob , the objects of C , which satisfy the following conditions: For every pair a b of objects, there is a collection

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