61. The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. sites and Web pages relating to the study of mathematics. This page contains sites relating to category theory/Homological Algebra. http://mathforum.org/library/topics/category_theory/

Browse and Search the Library Home Math Topics Algebra Modern Algebra : Cat. Theory/Homolgcl Alg. Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category Category Theory, Homological Algebra - Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to category theory, a comparatively new field of mathematics that 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. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>> All Sites - 19 items found, showing 1 to 19 Applied and Computational Category Theory - RISC-Linz, Austria A brief history and description of category theory, and some related links. From the Research Institute for Symbolic Computation. ...more>> Categories, Quantization, and Much More - John Baez

62. Category Theory category theory. category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. http://www.fact-index.com/c/ca/category_theory.html

Main Page See live article Alphabetical index Category theory Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "abstract nonsense". See list of category theory topics for a breakdown of the relevant Wikipedia pages. Table of contents 1 Background 2 Historical notes 3 Categories 3.1 Definition ... 11 Literature Background A category attempts to capture the essence of a class of related mathematical objects, for instance the class of groups . Instead of focusing on the individual objects (groups) as has been done traditionally, the morphisms, i.e. the structure preserving maps between these objects, are emphasized. In the example of groups, these are the group homomorphisms . Then it becomes possible to relate different categories by functors , generalizations of functions which associate to every object of one category an object of another category and to every morphism in the first category a morphism in the second. Very commonly, certain "natural constructions", such as the fundamental group of a topological space , can be expressed as functors. Furthermore, different such constructions are often "naturally related" which leads to the concept of

63. CTCS99 8th conference on category theory and Computer Science. Edinburgh, Scotland, UK; 1012 September 1999. http://www.dcs.ed.ac.uk/home/ctcs99/

Call for participation CTCS'99, 10-12 September 1999, Edinburgh, Scotland CTCS '99 is the 8th conference on Category Theory and Computer Science . The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory. While the emphasis is upon applications of category theory, it is recognized that the area is highly interdisciplinary. Previous meetings have been held in Guildford (Surrey), Edinburgh, Manchester, Paris, Amsterdam, Cambridge, and S. Margherita Ligure (Genova). Conference proceedings will appear in Electronic Notes in Theoretical Computer Science . Paper copies of the proceedings will be available to participants at the conference. Invited speakers: R. Hasegawa , Univ. of Tokyo (Japan) P. Freyd , Univ. of Pennsylvania (USA) M. Fiore , Univ. of Sussex (UK) D. Smith , Kestrel Institute (USA) Programme committee: J. Adamek TU Braunschweig (Germany) N. Benton Microsoft Res., Cambridge (UK) R. Blute U. Ottawa (Canada) T. Coquand Chalmers (Sweden) M. Escardo

64. Kernel (category Theory) Kernel (category theory). In particular, kernel pairs can be used to interpret kernels in monoid theory or ring theory in categorytheoretic terms. http://www.fact-index.com/k/ke/kernel__category_theory_.html

Main Page See live article Alphabetical index Kernel (category theory) In category theory and its applications to other branches of mathematics kernels are a generalization of the kernels of group homomorphisms and the kernels of module homomorphisms and certain other kernels from algebra . Intuitively, the kernel of the morphism f A B is the "most general" morphism k K A which, when composed with f , yields zero. Note that kernel pairs and difference kernels (aka binary equalisers) sometimes go by the name "kernel"; while related, these aren't quite the same thing and are not discussed in this article. Table of contents 1 Definition 2 First properties 3 Examples 4 Relation to other categorical concepts ... 5 Relationship to algebraic kernels Definition Let C be a category . In order to define a kernel in the general category-theoretical sense, C needs to have zero morphisms. In that case, if f A B is an arbitrary morphism in C , then a kernel of f is an equaliser of f and the zero morphism from A to B . In symbols: ker f = eq ( f A B To be more explicit, the following

65. Lambda The Ultimate Category Theory For Beginners (slides) category theory for Beginners (slides). category theory for Beginners (slides) started 7/14/2003; 92024 AM last post 7/16/2003; 51355 PM. http://lambda.weblogs.com/discuss/msgReader$7643

Lambda the Ultimate The Programming Languages Weblog - join today! Home FAQ Feedback Departments ... Genealogical Diagrams Members Join Now Login Category Theory for Beginners (slides) Previous topic Next topic Category Theory for Beginners (slides) started 7/14/2003; 9:20:24 AM - last post 7/16/2003; 5:13:55 PM Isaac Gouy - Category Theory for Beginners (slides) 7/14/2003; 9:20:24 AM (reads: 1160, responses: 15) Category Theory for Beginners* (slides) • What is Category Theory? • Why should we be interested in Category Theory? • How much Category Theory is it useful to know? • What kinds of things can you do with Category Theory in Software Engineering? Chris Rathman - Re: Category Theory for Beginners (slides) 7/14/2003; 10:18:45 AM (reads: 1176, responses: 1) Most excellent. Ought to be posted to front page. :-) Marc Hamann - Re: Category Theory for Beginners (slides) 7/14/2003; 10:25:49 AM (reads: 1167, responses: 0) A nice little presentation. The stuff about a category theoretic view of specifications is interesting. For someone who liked the style of intro material in this presentation and wants to learn more, I would recommend "Conceptual Mathematics" by Lawvere and Schanuel, or "Sets for Mathematics" by Lawvere and Rosebrugh.

66. ATCAT Dalhousie University, Halifax. Weekly meetings. http://www.mscs.dal.ca/~pare/atcat.html

@CAT @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@mscs.cs.dal.ca 2002-2003 Participants List of talks Upcoming talks The Naming of Cats - T.S.Eliot

67. Lambda The Ultimate Category Theory For Non-mathematicians category theory for nonmathematicians. category theory for non-mathematicians started 8/20/2001; 14822 PM - last post 8/27/2001; 20414 AM. http://lambda.weblogs.com/discuss/msgReader$1696

Lambda the Ultimate The Programming Languages Weblog - join today! Home FAQ Feedback Departments ... Genealogical Diagrams Members Join Now Login Category theory for non-mathematicians Previous topic Next topic Category theory for non-mathematicians started 8/20/2001; 1:48:22 PM - last post 8/27/2001; 2:04:14 AM Ehud Lamm - Category theory for non-mathematicians 8/20/2001; 1:48:22 PM (reads: 3625, responses: 4) Category theory for non-mathematicians Book suggestions on comp.lang.functional. Posted to Misc-Books by Ehud Lamm on 8/20/01; 1:48:38 PM jon fernquest - Re: Category theory for non-mathematicians 8/21/2001; 12:56:54 AM (reads: 2179, responses: 0) Are there any books in which programming and the math (category theory) are developed in parallel? Like a book on category theory with actual ML code? All the books I've seen are either pure abstract math (i.e. theorem / proof) or functional programming with at most a cursory reference to category theory, like "A fold function is a catamorphism." Also is there any glossary out there that relates different language constructs and category theory terminology? Like "Monad" seems to be strongly attached to Haskell and the writings of Wadler. Never seen "Monad" in CAML code. Monads seem to have a parallel in Scheme closures, but I've never seen anyone make this analogy. Cheers

68. CRTC -- Montréal -- Seminars Timetable. http://www.math.mcgill.ca/rags/seminar/

Category Theory Research Center Seminars scheduled in 2003-2004 Tuesday, 16 September 2003 2:30 - 4:00 John Kennison Looking for Pathological Electrical Flows through a Graph Tuesday, 23 September 2003 2:30 - 4:00 John Kennison The cyclic spectrum of a dynamic system 28 October 2003 2:30 - 4:00 M. Barr On absolutely CR-epic spaces. Abstract: A completely regular space X is called absolute CR-epic if whenever X is embedded into another completely regular space Y, the induced map C(Y) > C(X) is an epimorphism in the category CR of commutative rings. For example, every space that is locally compact and sigma-compact is an absolute CR-epic. This is joint work with Robert Raphael and Grant Woods. Postponed to 27 January 2004 (Was: 18 November 2003) 2:30 - 4:00 M. Barr Sub-pregroups of the Lambek pregroup 25 November 2003 2:30 - 4:00 Isidore Fleischer (CRM Montreal and Univ. of Windsor) Amalgamation in algebraic logic. (Must the Cat be let out of the bag?)

69. CompCat At Bangor University of Wales, Bangor School of Informatics. Computational category theory. This site is part of The Computational category theory Project. Groups. http://www.bangor.ac.uk/ma/research/compcat/

University of Wales, Bangor - School of Informatics Computational Category Theory This site is part of The Computational Category Theory Project. Groups Currently connected with this project are: Contact: Bob Walters at: Walters@fis.unico.it Mount Allison University, Canada Contact: Bob Rosebrugh at: RRosebrugh@mta.ca This group Contact: Ronnie Brown at: R.Brown@bangor.ac.uk Goals and Method 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. New versions will be announced on the Categories Mailing List. Background to Activities at Bangor Participants Background Papers Software developed at Bangor XMOD - (Wensley/Alp) GAP3 package for crossed modules and cat1-groups (currently being converted to GAP4.1); KAN - (Heyworth) GAP3 package for Kan extensions of actions of categories (currently being converted to GAP4.1).

70. (Canada) University Of Calgary Calgary Peripatetic Research Group in Logic and category theory alternates between departments of mathematics, philocophy, and computer science; meets weekly. http://pages.cpsc.ucalgary.ca/~luigis/CPRGLCC/

Calgary Peripatetic Research Group on Logic and Category Theory Meetings on Logic and Category Theory to be held in the Philosophy Mathematics and Computer Science Departments of the University of Calgary TIME: Monday 2:10pm (weekly) , PLACE: ICT 616 (or as arranged). Fall 2001: next seminar, incoming seminars, past seminars. Participants For talk titles, abstracts, comments etc. contact Luigi Santocanale

71. Computational Category Theory Welcome to the Computational category theory Project. The Programs. To access the Computational category theory programs go to this directory. http://www.cs.man.ac.uk/~david/categories/

Welcome to the Computational Category Theory Project Computational Category Theory is an implementation of concepts and constructions from category theory in the functional programming language Standard ML. The Manual For full details of the project, there is a copy of the manual (in PDF or Postscript) available here The Programs To access the Computational Category Theory programs go to this directory . There is a Readme file giving instructions on compiling and running the programs. Any comments? Please email me at david @ cs.man.ac.uk This page is maintained by myself, email address above. Last updated 21-05-03

72. Manchester Uni Formal Methods Group - Category Theory And Logic In Computation category theory and Logic in Computation. Principal Contributions of logic and category theory to the semantics of computation. Studies http://www.cs.man.ac.uk/fmethods/projects/category-theory-and-logic.html

Category Theory and Logic in Computation Principal investigator: David E Rydeheard (david@cs.man.ac.uk) The ongoing research in this area covers: The implementation of category theory as functional programs - an axiomatisation of the notion of computability relevant to this implementation. Category theory as a general framework for logic: Logical frameworks based on categorical logic - modular construction of logics. The application to program logics and program development methods. Implementation as a categorical `program development environment'. Contributions of logic and category theory to the semantics of computation. Studies in the structure of programming languages, especially type structure. Funding: Two EU projects - "CLICS-II" and "Types for Proofs and Programs". FM Home Page

73. INTERNATIONAL CATEGORY THEORY CONFERENCE(CT04) INTERNATIONAL category theory CONFERENCE(CT04). July 2004. All those interested in category theory and its applications are welcome. http://www.pims.math.ca/science/2004/CT04/

74. ATCAT @CAT. @CAT (Atlantic category theory Seminar) is our weekly seminar in which topics related to category theory (algebra, logic, topology, category theory itself http://www.mathstat.dal.ca/~pare/atcat.html

@CAT @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@mscs.cs.dal.ca 2002-2003 Participants List of talks Upcoming talks The Naming of Cats - T.S.Eliot

75. PlanetMath: Category Theory category theory, (Topic). Introduction. As a tool, category theory allows mathematicians to focus on the morphisms between objects rather than their elements. http://planetmath.org/encyclopedia/CategoryTheory.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Corrections talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information Docs Classification News Legalese ... TODO List category theory (Topic) Introduction Much of contemprary mathematics studies algebraic structures of one sort or another: rings groups vector spaces and many others. More generally, the idea of a set with some structure is very general: topological spaces differentiable manifolds graphs and so on. Each of these kinds of things has a notion of a function that respects the structure: group and ring homomorphisms linear transformations continuous functions differentiable functions , graph homomorphisms category was introduced. A category has two parts: a collection of objects, and a notion of morphism between two objects. These morphisms are required to have an associative composition law, and there are a few other conditions, but a category is a very general notion. Each of the examples listed above forms a category. Some very simple objects can form categories; the objects need not have meaningful elements, and the morphisms need not be functions.

76. Category Theory For Computer Science category theory for Computer Science. Autumn 2002 computer science category theory in programming language semantics and design. http://www.daimi.au.dk/~nygaard/CTfCS/

Category Theory for Computer Science Autumn 2002 - Department of Computer Science University of Aarhus News Lectures ... People News The course has terminated. Merry Christmas! Lectures Mondays, 12-14 in the r3 meeting room. December 9th A coalgebraic treatment of automata. Presented by Saurabh Agarwal. December 2nd Infinite data structures, coalgebra, and coinduction. Presented by Michael Westergaard ( slides November 25th Finite data structures, algebra, and induction. Presented by Henning Korsholm Rohde ( slides November 18th Transition systems generalised into presheaves. Presented by Marco Carbone. November 11th Exercises related to last week's lecture. Designing subtyping disciplines in programming languages. Presented by Branimir Lambov. November 4th Exercise related to last week's lecture. Effects in functional programming handled by monads. Presented by Karl Kristian Krukow ( slides October 28th Modelling recursive types. Presented by Mads Sig Ager (

77. Image (category Theory) - Encyclopedia Article About Image (category Theory). Fr encyclopedia article about Image (category theory). Image (category theory) in Free online English dictionary, thesaurus and encyclopedia. http://encyclopedia.thefreedictionary.com/Image (category theory)

Dictionaries: General Computing Medical Legal Encyclopedia Image (category theory) Word: Word Starts with Ends with Definition Given a category it is used informally to mean a class of things, as in "the category of all living things" in philosophy: Aristotle classified everything into 10 famous categories Click the link for more information. , two objects Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "abstract nonsense". See list of category theory topics for a breakdown of the relevant Encyclopedia pages. Background A category attempts to capture the essence of a class of related mathematical objects, Click the link for more information. in it, X and Y and a morphism In mathematics, a category is given by two pieces of data: a class of objects and, for any two objects X and Y , a set of morphisms from X to Y . Morphisms are often depicted as arrows between those objects. In the case of a concrete category, X and Y are sets of some kind and a morphism f is a function from X to Y satisfying some condition; this example supplies the notation

78. Category Theory - Encyclopedia Article About Category Theory. Free Access, No Re encyclopedia article about category theory. category theory in Free online English dictionary, thesaurus and encyclopedia. category theory. http://encyclopedia.thefreedictionary.com/category theory

Dictionaries: General Computing Medical Legal Encyclopedia Category theory Word: Word Starts with Ends with Definition Category theory is a mathematical Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "abstract nonsense". See list of category theory topics This is a list of category theory topics , by Encyclopedia page. Specific categories Category of sets Concrete category K-Vect Category of topological spaces Category of metric spaces Category of preordered sets Category of abelian groups Category of magmas Category of medial magmas Objects Initial object Terminal object Zero object Subobject Group object Click the link for more information.

79. Category Theoretic Perspectives On The Foundations Of Mathematics Problems for category theory in Classical Set Theoretic Foundations. Some Links related to category theory and the Foundations of Mathematics. http://www.rbjones.com/rbjpub/philos/maths/faq004.htm

Category Theoretic Perspectives on the Foundations of Mathematics See also the Categories Home Page I don't pretend to understand what category theory has to say about the foundations of mathematics, but I would rather like to understand. To that end these notes are compiled recording my impressions, such as they are, about the why Category theorists have misgivings about classical set theory as a foundation for mathematics and what (if anything) they would like to offer in its stead. problems solutions links Problems for Category Theory in Classical Set Theoretic Foundations Doing Category Theory in Set Theory Many categories are categories of all examples of a particular kind of mathematical structure (or of all models of a particular theory). Such collections are problematic in set theory in the same way as the set of all sets. In consistent set theoretic foundations based on the iterative conception of set they can be proven not to exist. Though there are techniques which can be employed to mitigate these difficulties, the solutions are not entirely satisfactory, and the view that set theory is not a natural context in which to do category theory may persist. For more on this kind of problem, see: Chapter 8 Introduction and Section 3 . Furthermore, certain kinds of construction which are important in category theory cannot reliably be done in set theory, for similar reasons, see

80. Online Encyclopedia - Category Theory , Encyclopedia Entry for category theory. See list of category theory topics for a breakdown of the relevant Wikipedia pages.......Encyclopedia http://www.yourencyclopedia.net/Category_theory.html

Encyclopedia Entry for Category theory Dictionary Definition of Category theory Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them. It is half-jokingly known as "abstract nonsense". See list of category theory topics for a breakdown of the relevant Wikipedia pages. Table of contents showTocToggle("show","hide") 1 Background 2 Historical notes 3 Categories 3.1 Definition ... 11 Literature Background A category attempts to capture the essence of a class of related mathematical objects, for instance the class of groups . Instead of focusing on the individual objects (groups) as has been done traditionally, the morphisms , i.e. the structure preserving maps between these objects, are emphasized. In the example of groups, these are the group homomorphisms . Then it becomes possible to relate different categories by functors , generalizations of functions which associate to every object of one category an object of another category and to every morphism in the first category a morphism in the second. Very commonly, certain "natural constructions", such as the fundamental group of a topological space , can be expressed as functors. Furthermore, different such constructions are often "naturally related" which leads to the concept of

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