Geometry.Net - Pure_And_Applied_Math: Category Theory

Theory And Applications Of Categories
An electronic journal of category theory. Full text, free.Category Science Math Algebra category theory Journals 4. A Note on Actions of a Monoidal Category G. Janelidze 6. Categorical domain theoryScott topology, powercategories, coherent categories Panagis Karazeris
http://www.tac.mta.ca/tac/

Extractions: A survey of definitions of n-category Tom Leinster, 1-70 abstract dvi dvi.gz ps ... A homotopy double groupoid of a Hausdorff space Ronald Brown, Keith A. Hardie, Klaus Heiner Kamps, Timothy Porter, 71-93 abstract dvi dvi.gz ps ... Entity-relationship-attribute designs and sketches Michael Johnson, Robert Rosebrugh and R.J. Wood, 94-112 abstract dvi dvi.gz ps ... pdf Emzar Khmaladze, 113-126 abstract dvi dvi.gz ps ... Exponentiability of perfect maps: four approaches Susan Niefield, 127-133 abstract dvi dvi.gz
Centre De Recherche En Théorie Des Catégories -- Montréal
What is category theory? category theory at McGill A personal account by Marta Bunge. category theory an expository
http://www.math.mcgill.ca/triples

Extractions: Category Theory Research Center Translation? Category Theory at McGill A personal account by Marta Bunge. Category Theory - an expository article from the Stanford Encyclopedia of Philosophy. A Brief Description of Category Theory from the RISC-Linz Category Theory page. Categories, Quantization, and Much More - an introduction by John Baez. (You might also explore his series "This Week's Finds in Mathematical Physics" which often has references to logic , category theory, and particularly n -category theory Toposes, Triples and Theories A classic text by M Barr and C Wells, now freely available on-line. Category Theory for Computing Science (Ordering information for another classic text by M Barr and C Wells, the current version published by the CRM.) Acyclic Models (Ordering information for a recent book by M Barr.) Texte d'Alexandre Grothendieck (in progress)
Category Theory
Stanford Encyclopedia of Philosophy category theory is a general mathematical theory of structures and sytems of structures.
http://plato.stanford.edu/entries/category-theory

Extractions: JUL 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. 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
Introduction To Category Theory
Lecture notes by Maarten M. Fokkinga introducing some important notions from category theory, in particul Category Science Math Algebra category theoryA Gentle Introduction to category theory the calculational approach. Maarten MFokkinga In these notes we present the important notions from category theory.
http://wwwhome.cs.utwente.nl/~fokkinga/mmf92b.html

Extractions: Maarten M Fokkinga In these notes we present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. What you probably will not acquire from these notes is the ability to recognise the concepts in your daily work when that differs from algorithmics, since we give only a few examples and those are taken from algorithmics. For such an ability you need to work through many, very many examples, in diverse fields of applications. Full paper (postscript version): here (80 pages). Bibtex data
18: Category Theory, Homological Algebra
In the "known maths" series.Category Science Math Algebra category theoryIntroduction. category theory, a comparatively new field of mathematics, providesa universal framework for discussing fields of algebra and geometry.
http://www.math.niu.edu/~rusin/known-math/index/18-XX.html

Extractions: POINTERS: Texts Software Web links Selected topics here Category theory, a comparatively new field of mathematics, 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. The word "category" is used to mean something completely different in general topology This is among the smaller areas in the Math Reviews database. Browse all (old) classifications for this area at the AMS. Textbooks, reference works, and tutorials
Applied And Computational Category Theory
A brief description of category theory, and some useful links.Category Science Math Algebra category theoryApplied and Computational category theory. A Brief History topology. However,soon category theory became a field in itself. The reason
http://www.risc.uni-linz.ac.at/research/category/

Extractions: A Brief History of Category Theory However, soon category theory became a field in itself. The reason for this is that it provides a unifying and economic mathematical modeling language. It lends itself very well to extracting and generalizing elementary and essential notions and constructions from many mathematical disciplines. Thanks to its general nature, the language of category theory enables one to "transport" problems from one area of mathematics, via suitable "functors", to another area, where the solution may be easier to find. Categories have successfully been applied in formulating and solving problems in topology, algebra, geometry and functional analysis. Moreover, in the sixties Lawvere started a project aiming at a purely categorical foundation of all mathematics, beginning with an appropriate axiomatization of the category of sets. This has led to a huge interest in and development of sheaf and topos theory. More recently, computer science discovered category theory. It quickly found applications in the field of algebraic semantics and the theory of (functional) programming languages; later, applications in automata theory followed suit. But not only did computer science benefit from using category theory; the functional programming language "ML", which is based on the semantics of polymorphic lambda calculus (a topic requiring category theory for a proper discussion), has in turn shown itself to be a suitable vehicle for explaining the language and concepts of category theory. Moreover, computer science and ML have made the inherent computational nature of category theory come out into the open.
Categories Home Page
Categories List. The category theory mailing list, moderated by Bob Rosebrugh. Manyof the people listed by Hypatia have interests in category theory.
http://www.mta.ca/~cat-dist/categories.html

Extractions: Usually, items of this sort sent to `categories@mta.ca' will not be posted. Policy: The moderator will not modify articles except for minor typographical and formatting changes, therefore no offensive or defamatory material should be sent (it will be returned and not posted), and inflammatory posts are discouraged. Nevertheless, wide latitude for vigorous debate is allowed. Return to top. M. Alsani has created a selected list of CT email, also sorted by thread, from August 1999 to February 2002 at http://north.ecc.edu/alsani/cat-dist2html/index.html A subject-sorted list of postings June 1994-December 1999 is at www.mta.ca/~cat-dist/catlist/
Categories Home Page
The category theory mailing list . moderated by Bob Rosebrugh.
http://www.mta.ca/~cat-dist

Extractions: Usually, items of this sort sent to `categories@mta.ca' will not be posted. Policy: The moderator will not modify articles except for minor typographical and formatting changes, therefore no offensive or defamatory material should be sent (it will be returned and not posted), and inflammatory posts are discouraged. Nevertheless, wide latitude for vigorous debate is allowed. Return to top. M. Alsani has created a selected list of CT email, also sorted by thread, from August 1999 to February 2002 at http://north.ecc.edu/alsani/cat-dist2html/index.html A subject-sorted list of postings June 1994-December 1999 is at www.mta.ca/~cat-dist/catlist/
Applications Of Category Theory To Computer Science
Mount Allison University, Sackville, NB, Canada; 812 June 1998.Category Science Math Algebra category theory Events Past EventsWorkshop Applications of category theory to Computer Science. June812, 1998 Mount Allison University, Sackville, NB, Canada. In
http://www.mta.ca/~cat-dist/ctss98/

Extractions: Sackville, NB, Canada In conjunction with the Category Theory Session at the Canadian Mathematical Society's Summer 1998 Meeting, see camel.math.ca/CMS/Events/summer98/ , there will be a workshop on the Applications of Category Theory to Computer Science, directed towards graduate students and young researchers. The arrival day Sunday, June 7, 1998 - residence accommodation will be available from June 6. The invited instructors are M. Barr (McGill) and R.F.C. Walters (Sydney). Residence accommodation will be available at Mount Allison University at a cost of
CTCS'02
category theory and Computer Science. University of Ottawa, Ontario, Canada; 1517 August 2002.Category Science Math Algebra category theory Events Past Eventscategory theory and Computer Science (CTCS'02) August 15th17th, 2002 Universityof Ottawa. and Graduate Student Preconference August 12-14, 2002
http://www.mathstat.uottawa.ca/lfc/ctcs2002/

Extractions: 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 developped 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. In addition to the usual three day conference, there will be a three day "preconference", which is designed to prepare students, both graduate and undergraduate, to participate in the conference. The preconference will take place from August 12-14.
Computational Category Category Theory Project
The aim of this project is the development of software on a wide variety of platforms for computing Category Science Math Algebra category theoryComputational category theory Project. Goals and Method. The aimof this project is the development of software on a wide variety
http://www.mcs.le.ac.uk/~ah83/compcat/

Extractions: Up: Anne's Home page 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. 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. R. F. C. Walters
Dynamic Directory - Science - Math - Algebra - Category Theory
Applied and Computational category theory A brief description of category theory, and some useful links.
http://www.maximumedge.com/cgi/dir/index.cgi/Science/Math/Algebra/Category_Theor

Extractions: Applied and Computational Category Theory - A brief description of category theory, and some useful links. Categorical Myths and Legends - An archive of stories about category theorists. Categories Home Page - Web page for the category theory mailing list. Categories, Quantization, and Much More - Introductory article by John Baez. Category Theory - This expository article is an entry in the Stanford Encyclopedia of Philosophy. Category Theory and Homological Algebra - In the "known maths" series. 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. 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 algebraic structures.
Applied And Computational Category Theory At RISC-Linz
Applied and Computational category theory at RISCLinz. NB this pagenot updated after Dec 1, 1999. Researchers (Responsible faculty
http://www.risc.uni-linz.ac.at/research/category/risc/

Extractions: NB: this page not updated after Dec 1, 1999. Researchers (Responsible faculty member: Jochen Pfalzgraf The people working in applied and computational category theory at RISC-Linz (faculty and students). Research topics A general description of the research area we are involved in. Seminar and Lectures The schedule of the seminar and the lectures organized at RISC-Linz in the field of applied and computational category theory. Publications The list of the publications of RISC-Linz members working in this area. Events Interesting conferences, meetings and other events related to the topic, held at RISC-Linz or elsewhere. Mails from the Category Theory Mailing List E-Mails from the Category Theory mailing list maintained and moderated by Bob Roseburgh, sorted by subject. Announcements of Positions (through the Category Theory Mailing List) Positions Announcements disseminated through the Category Theory mailing list. Other Categorical Links Some other pages around the world with similar research interests: The Category Home Page at Mount Allison University, Canada
OctoberFest 99: Centre De Recherche En Théorie Des Catégories -- Montréal
McGill University, Montreal, Canada; 1617 October 1999.Category Science Math Algebra category theory Events Past EventsCTRC Centre de Recherche en Théorie des Catégories Montréal category theory Research Center. category theory OctoberFest.
http://www.math.mcgill.ca/triples/octoberfest99.html

Extractions: 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
Alsani's Descent & Category Theory WebPage!
Maintained by M. Alsani.Category Science Math Algebra category theory This page is merely a launching pad to sites of interest in Descent or CategoryTheory. Picture of some people interested in category theory
http://north.ecc.edu/alsani/descent.html

Extractions: M. Alsani; alsani@ecc.edu This page is merely a launching pad to sites of interest in Descent or Category Theory. Selected Category Theory E-mail from the Category Theory mailing list Category Theory Archives from the Front for the Mathematics ArXiv site Category Theory Stanford Encyclopedia of Philosophy - Archives CATEGORIES HOME PAGE Bob Rosebrugh Ccard 2.0 - or : How to make fun out of something highly abstract. TEORIA E APPLICAZIONI DELLE CATEGORIE University of Genoa, Italy Kategorielle Methoden in Algebra und Topologie Texte d'Alexandre Grothendieck (in progress) Categorical Geometry Zhaohua Luo page F. William Lawvere page John Duskin page Toposes, Triples and Theories - A classic text by M Barr and C Wells Descent Theory and its Higher Dimensional Analogues Descent theory and Amitsur cohomology of adjoint functors Slides by Dragos Stefan Geometric and Logical Aspects of Descent Theory Oberwolfach 1995. Descent Theory of Coalgebras and Hopf Algebras DESCENT OF COHERENT SHEAVES AND COMPLEXES TO GEOMETRIC INVARIANT THEORY Etale descent for two-primary algebraic K-theory of totally imaginary number fields , by J. Rognes and C. Weibel A DESCENT THEOREM IN TOPOLOGICAL K-THEORY , by Max Karoubi Category Theory at McGill Marta Bunge page W. Tholen Page
BIBLIOGRAPHY About DESCENT And CATEGORY THEORY!
BIBLIOGRAPHY about category theory. bysame \book *Autonomous categories; \bysame\book category theory for Computing Science \publaddr Prentice Hall \yr 1995;
http://north.ecc.edu/alsani/catbib.html

Extractions: BIBLIOGRAPHY about DESCENT THEORY from W. Tholen home page. Monades et Descente Selected Topics in Algebra An Outline of a Theory of Higher Dimensional Descent The Theory of Descent Triples and Descent An Extension of the Galois Theory of Grothendieck Theory of Categories over a Base Topos Descent Theory for Toposes Effective Descent Morphisms and Effective Equivalence Relations Introduction to Affine Group Schemes BIBLIOGRAPHY about CATEGORY THEORY F. W. Lawvere publications: http://www.acsu.buffalo.edu/~wlawvere Back to Descent and Category Theory WebPage
Comcat
The aim of the project is the development of software on a wide variety of platforms for computing Category Science Math Algebra category theory
http://www.unico.it/~walters/comcat/comcatproj.html

Extractions: 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: 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.
Category Theory
X Y Z category theory. category theory is a general mathematicaltheory of structures and sytems of structures. It allows us
http://setis.library.usyd.edu.au/stanford/archives/fall1997/entries/category-the

Extractions: A B C D ... Z 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. 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
Structuralism, Category Theory And Philosophy Of Mathematics
By Richard Stefanik (Washington MSG Press,1994).Category Society Philosophy Philosophy of MathematicsStructuralism, category theory and Philosophy of Mathematics by RichardStefanik (Washington MSG Press,1994). Is the philosophy
http://www.mmsysgrp.com/strctcat.htm
MATHEMATICAL STRUCTURES RESEARCH
Research topics include mathematical models and theories in the empirical sciences, models and theories Category Society Philosophy Philosophy of Mathematics Structuralism, category theory and Philosophy of Mathematics . MSG Press, 1994;Suppes, Patrick. Introduction to Logic. category theory and Categorical Algebra.
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

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