Geometry.Net - Pure_And_Applied_Math: Category Theory

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

Extractions: Software: Graphical Database for Category Theory (GDCT) Java application - Version 2.0 (July 2002) mathcs.mta.ca/research/rosebrugh/gdct/ Category Theory Database Tools Java applet - limited, 1998 version of GDCT at www.mta.ca/~rrosebru/mathcs/javasource/index.htm A Database of Categories - a menu-based C program (1995). Member of the Computational Category Theory Project
Abstract Algebra:Category Theory - Wikibooks
category theory From MathWorldThe objects studied in category theory are called categories. SEE ALSO Category . category theory. From MathWorldA Wolfram Web Resource.
http://en.wikibooks.org/wiki/Abstract_algebra:Category_theory

Extractions: Category theory is the study of categories , which are collections of objects and morphisms (or arrows), or from one object to another. edit A category is a graph with two functions u and c , and , where C is the class of vertices in the graph which we shall call objects , and C is the class of edges in which we shall from here on in refer to as arrows or morphisms . The function u then takes an object a to its associated identity function i d a , which maps a onto a . The function c takes pairs of arrows to their composition. For the sake of brevity, we will define Categories have the following properties: edit , the category whose objects are sets, and whose morphisms are maps between the sets. The category whose objects are open subsets of and whose morphisms are continuous (differentiable, smooth) maps between them.
Mathematical Structures In Computer Science
Focuses on the application of areas such as logic, algebra, geometry and category theory to theoretical computer science.
http://uk.cambridge.org/journals/msc/
Category Theory -- From MathWorld
category theory Free Product Pullback Map Coequalizer Freyd s Theorem Pushforward Map Commutative Diagram Functor Schur Functor
http://mathworld.wolfram.com/topics/CategoryTheory.html
Theory And Semantics Group
Centred around mathematical models of a variety of languages and logics, using techniques such as structural operational semantics, linear logic, domain theory and category theory. Strong links with Logic and Set Theory in the Pure Mathematics Department.
http://www.cl.cam.ac.uk/Research/TSG/

Extractions: The work of the Theory and Semantics Group is centred around mathematical models of a variety of languages and logics. These models are intended to be used as a basis for specification and verification, and as a tool for clarifying programming concepts. We use techniques such as structural operational semantics, linear logic, domain theory and category theory. Work is in progress on the underlying mathematical structures of these, and on their application to the study of higher order typed programming languages such as Standard ML, to object-based languages, to foundational languages for concurrent, distributed and mobile computation, to hardware description languages, and to security problems. Work is also being undertaken on the analysis of programming languages in the setting of abstract interpretation and on practical optimising compilation for imperative and functional languages. Related research is undertaken within the Automated Reasoning Group . We also have links with the Logic Seminar at DPMMS (Dept of Pure Mathematics and Mathematical Statistics).
Category Theory Authors/titles Recent Submissions
Subjclass Representation Theory; category theory MSC-class 16G70; 18G20; 20E15 Subj-class Quantum Algebra; category theory; Rings and Algebras
http://arxiv.org/list/math.CT/recent
[math/0106240] Topology And Higher-Dimensional Category Theory: The Rough Idea
Subjclass category theory; Algebraic Topology; Quantum Algebra. Higher-dimensionalcategory theory is the study of n-categories, operads, braided monoidal
http://arxiv.org/abs/math.CT/0106240

Extractions: Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the higher-dimensional diagrams one draws to represent these structures can be taken quite literally as pieces of topology. Examples of this are the braids in a braided monoidal category, and the pentagon which appears in the definitions of both monoidal category and A_infinity space. I will try to give a Friday-afternoonish description of some of the dreams people have for higher-dimensional category theory and its interactions with topology. Grothendieck, for instance, suggested that tame topology should be the study of n-groupoids; others have hoped that an n-category of cobordisms between cobordisms between ... will provide a clean setting for TQFT; and there is convincing evidence that the whole world of n-categories is a mirror of the world of homotopy groups of spheres. References and citations for this submission:
Category Theory For Computing Science
This book is a textbook in basic category theory, written specifically to We expound the constructions we feel are basic to category theory in the
http://www.cwru.edu/artsci/math/wells/pub/ctcs.html

Extractions: by Michael Barr and Charles Wells Category Theory for Computing Science is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. You may read the excerpts from the Preface to find out more about it. The third edition is now available from Centre de recherches mathématiques , or by email to sales@crm.umontreal.ca . This edition contains all the material dropped from the second edition (with corrections) and the answers to all the exercises. It is cheaper, too; it costs only about US$ , postpaid (surface mail) anywhere in the world. Some of the chapters in the first edition were dropped from the second edition in order to make room for new material. Revised and corrected versions of the omitted chapters may now be found in an electronic supplement to the text. We also provide corrections and additions to the first edition and corrections to the second edition This book is a textbook in basic category theory, written specifically to beread by researchers and students in computing science. We expound the constructions we feel are basic to category theory in the context of examples and applications to computing science.
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

Extractions: Category Theory Theoretical Computer Science ... WWW Research Sites 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
ATCAT
@CAT (Atlantic category theory Seminar) is our weekly seminar in which topicsrelated to category theory (algebra, logic, topology, category theory itself,
http://www.mathstat.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@mathstat.dal.ca 2005-2006 Participants
Ramifications Of Category Theory, 2003
Ramifications of category theory, 2003. Firenze, November 2003. Index A B C D E F G H I J K L M N O P Q R S T U
http://andrej.com/mathematicians/group/ramcat2003.html
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/

Extractions: Email: Ian.Stark@ed.ac.uk Phone: +44 (131) 650 5143 (Work) +44 (131) 228 4101 (Home) Fax: Office: JCMB 2506 Papers Talks My research is on mathematical models for programming languages and concurrent systems; in particular reasoning about name generation and mobile code Advanced Research Fellowship . I am also involved with the following research projects: PhD students: I am second supervisor for Rob Atkey Alex Blewitt Jonathan Cook (completed 2004), Shin-Ya Katsumata (completed 2005), Francis Tang completed 2002 ) and Jeremy Yallop Some keywords: mathematical logic, category theory, type theory, principles of programming languages, denotational semantics, operational semantics, domain theory, game semantics, functional programming, Standard ML, Java, process calculi, pi-calculus, nu-calculus, reasoning with names. I am giving no undergraduate lecture courses for the duration of my research fellowship. Here are some past courses.
School On Category Theory And Applications
University of Coimbra, Portugal; 1317 July 1999.
http://www.mat.uc.pt/~scta/
Category Theory
Math reference, an introduction to category theory.
http://www.mathreference.com/cat,intro.html

Extractions: Use the arrows at the bottom to step through Category Theory. Introduction Much of mathematics involves pattern recognition, followed by generalization, then the swift application of the general to a problem that has not been seen before. Let me couch this in terms of computer programming, since I have been a professional programmer for 20 years. You write a ream of software to accomplish a certain task, and you feel like you've been here before. No, you didn't write this exact code before, line for line, but you wrote something very similar last year. You go back through your archives and dig out your old code. It does almost exactly what you want, with a few minor changes. You decide to write one program that handles both tasks. You'll need a couple parameters to accommodate the variations between tasks, but there is so much commonality; a dual-use program is the only way to go. You explain to your boss that you "Want to do it right." You want to build a flexible program that will handle both tasks. There will be less code over all, and fewer bugs, and if a bug is found, you can fix it once, not twice. But it will take a little longer to get the job done, because you're building a useful infrastructure, instead of solving today's problem as quickly as possible. You'll also need to run regression tests on the first task, to make sure the new program is handling it properly. That'll be another week, if nothing goes wrong.
Alissa S. Crans
Loyola Marymount University. Higherdimensional algebra Lie theory with elements of category theory, knot theory and Lie algebra cohomology. Publications, thesis.
http://myweb.lmu.edu/acrans/

Extractions: Department of Mathematics Loyola Marymount University 1 LMU Drive, Suite 2700 Los Angeles, CA 90045 Phone: Fax: Mathematics Curriculum Vitae **For the 2005-2006 academic year, I will be a VIGRE Ross Assistant Professor in the Department of Mathematics of The Ohio State University.** Many people who have never had occasion to learn what mathematics is confuse it with arithmetic and consider it a dry and arid science. In actual fact it is the science which demands the utmost imagination. One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit... It seems to me that the poet must see what others do not see, must see more deeply than other people. And the mathematician must do the same.
Category Theory And Computer Science
category theory and Computer Science 1989 Manchester, UK. David H. Pitt, David E.Rydeheard, Peter Dybjer, Andrew M. Pitts, Axel Poigné (Eds.) Category
http://www.informatik.uni-trier.de/~ley/db/conf/ctcs/

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

Extractions: fax: (381 11) 186 105 email: kosta@mi.sanu.ac.yu Curriculum Vitae 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).
Category Theory And Computer Science 1989
3. category theory and Computer Science 1989 Manchester, UK Applications ofProof Theory to category theory In a Computer Scientist Perspective.
http://www.informatik.uni-trier.de/~ley/db/conf/ctcs/ctcs89.html

Extractions: David H. Pitt David E. Rydeheard Peter Dybjer Andrew M. Pitts (Eds.): Category Theory and Computer Science, Manchester, UK, September 5-8, 1989, Proceedings. Lecture Notes in Computer Science 389 Springer 1989, ISBN 3-540-51662-X BibTeX DBLP Giuseppe Longo : Coherence and Valid Isomorphism in Closed Categories - Applications of Proof Theory to Category Theory In a Computer Scientist Perspective. 1-4 BibTeX Ugo Montanari Daniel Yankelevich : An Algebraic View of Interleaving and Distributed Operational Semantics for CCS. 5-20 BibTeX Ross Casley Roger F. Crew Vaughan R. Pratt : Temporal Structures. 21-51 BibTeX Eugene W. Stark : Compostional Relational Semantics for Indeterminate Dataflow Networks. 52-74 BibTeX Luca Cardelli John C. Mitchell : Operations in Records. 75-81 BibTeX John Hughes : Projections for Polymorphic Strictness Analysis. 82-100 BibTeX Eugenio Moggi : A Category-theoretic Account of Program Modules. 101-117 BibTeX G. C. Wraith : A Note on Categorical Datatypes. 118-127 BibTeX Kent Petersson Dan Synek BibTeX ... Thomas Streicher : Independence Results for Calculi of Dependent Types. 141-154
CTCS'04
CTCS 04 is the tenth conference on category theory and Computer Science. While the emphasis is on applications of category theory, it is recognized that
http://www.itu.dk/research/theory/ctcs2004/

Extractions: 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.
Category Theory Course 2004
In category theory one may express constructions of mathematics such as products (or category theory also provides a formal setting for reasoning about
http://www.itu.dk/people/mogel/catcourse/

Extractions: A category consists of a class of objects and a class of morphisms. Examples are the category of rings with ring homomorphisms, and the category of topological spaces with continous maps as morphisms. In category theory one may express constructions of mathematics such as products (or more generally limits) and reason about them in a general setting. Category theory also provides a formal setting for reasoning about interactions between categories using the concepts of functors and natural transformations. Our main interest in category theory, however, comes from its applications to computer science and logic. In computer science for example, category theory can be used as a setting for models of programming languages. This course will cover: Categories, functors, natural transformations, Yoneda Lemma, limits and colimits, adjunctions, monads and algebras. There will also be a short introduction to categorical logic interpreting regular logic in a regular category, and showing how to use regular logic as an internal language for reasoning about regular categories. Likewise we show how to interpret simply typed lambda calculus in cartesian closed categories. Finally, the last section of the notes is classic material on the category of complete partial orders and the solution of recursive domain equations. There will be no real lectures, but we will meet once a week for about an hour to discuss exercises at the black board. The students are expected to read the material before the weekly meeting and to prepare a presentation of the exercises at the blackboard.

41-60 of 126 Back | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Next 20