Geometry.Net - Pure_And_Applied_Math: Category Theory

Papers In Category Theory And Other Areas
Papers in category theory and other areas. This bibliography is apart of the Computer Papers in category theory and other areas.
http://liinwww.ira.uka.de/bibliography/Theory/kstokker.html

Extractions: Computer Science Bibliographies Up: Bibliographies on Theory/Foundations of Computer Science Collection Home Papers in category theory and other areas About Browse Statistics Number of references: Last update: January 9, 1995 Number of online publications: Supported: no Most recent reference: Search the Bibliography Query: Options case insensitive Case Sensitive partial word(s) exact online papers only Results Citation BibTeX Count Only Maximum of matches Help on: [ Syntax Options Improving your query Query examples Austria Abstract: This is just a collection of papers I encountered in my quest for finding a categorical model for critical-pair/completion procedures. It is not even nearly exhaustive in any subject, but concentrates mainly on topics in category theory, rewriting, and computer algebra. Keywords: category theory, rewriting, computer algebra
Johnson: Category Theory
category theory. category theory is a branch of pure mathematics and althoughthe work described here is basic research it is very application driven.
http://www.comp.mq.edu.au/~mike/ct.html

Extractions: Category theory is a branch of pure mathematics and although the work described here is basic research it is very application driven. The application areas include homotopy theory, computer science, universal algebra and coherence theorems. for general information there is a category theory page on the web which includes information about conferences, web sites, the category theory bulletin board, and the electronic journal Theory and Applications of Categories . If you wish to write category theory you will need to be able to produce reasonably sophisticated diagrams and will probably want to look at the XY-Pic macros for use with LaTeX. If you would like to know more about my own work here is a brief discussion of n-categories and pasting , and some publications
Category Theory (advanced)
Texts Mac Lane and Moerdijk Coverage intro to topos theory withapplications. Philosophy. research content. Syllabus may also be
http://www.comp.mq.edu.au/~mike/catcourseadv.html
Category Theory
(category theory). F. Borceux, Handbook of Categorical Algebra 13.GM Kelly, Basic Concepts of Enriched category theory. Topos Theory.
http://www.kyoto-su.ac.jp/~hxm/categorical/ct/
Categories
Introductory article by John Baez.Category Science Math Algebra category theory (In fact, MacLane said I did not invent category theory to talk aboutfunctors. category theory is popular among algebraic topologists.
http://math.ucr.edu/home/baez/categories.html

Extractions: 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.) What is a category? Well, a category consists of a set of
Week68
Goldblatt's book teaches you all the category theory you need to learnabout topoi but for people who already know some category
http://math.ucr.edu/home/baez/week68.html

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

Extractions: 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
Casual Category Theory At BRICS
Casual category theory BRICS, University of Aarhus, News EventsPeople Literature. Viewable with Any Browser Valid HTML 4.01!
http://www.brics.dk/Activities/CCT/
Casual Category Theory - Fall 2001
BRICS LogoCasual category theory. .. is a informal study groupfor researcher interested in category theory. The new URL is
http://www.brics.dk/~varacca/CCT/
Category Theory Authors/titles Recent Submissions
Similar pages category theory resourcescategory theory resources. Recommended References. see index for totalcategory for your convenience Best Retirement Spots Teacher
http://xxx.lanl.gov/list/math.CT/recent
Papers By AMS Subject Classification
No papers on this subject. 18XX category theory, homological algebra/ Classification root. 18-00 General reference works (handbooks
http://im.bas-net.by/mathlib/en/ams.phtml?parent=18-XX
Category Theory
category theory. Research / Miscellaneous category theory Il sito,curato da Luca Mauri, fornisce risorse e informazioni sulla teoria
http://lgxserver.uniba.it/lei/logica/lgcat_th.htm

Extractions: "The journal Theory and Applications of Categories will disseminate articles that significantly advance the study of categorical algebra or methods, or that make significant new contributions to mathematical science using categorical methods. The scope of the journal includes: all areas of pure category theory, including higher dimensional categories; applications of category theory to algebra, geometry and topology and other areas of mathematics; applications of category theory to computer science, physics and other mathematical sciences; contributions to scientific knowledge that make use of categorical methods.". Il Journal distribuito gratuitamente via WWW/ftp, dopo essersi registrati. Related Fields SWIF
Re: Category Theory <-> Lambda Calculus?
Re category theory lambda calculus? Subject Re category theory - lambdacalculus? Next by thread Re category theory - lambda calculus?
http://www.lns.cornell.edu/spr/2001-03/msg0031750.html

Extractions: Date Prev Date Next Thread Prev Thread Next ... Thread Index http://www.uq.net.au/~zzdkeena/Lambda/ Follow-Ups From: References From: From: From: baez@galaxy.ucr.edu (John Baez) Prev by Date: Re: Direct Products of Hilbert Spaces Next by Date: Re: categorification of groups and related Prev by thread: Next by thread: Index(es): Date Thread
Category Theory (M24)
category theory (M24). E. Cheng Category Three volumes which togetherprovide a comprehensive modern account of category theory. Clearly
http://www.maths.cam.ac.uk/CASM/courses/descriptions/node26.html

Extractions: Next: Set Theory (M24) Up: Logic Previous: Logic E. Cheng Category theory begins with the observation (Eilenberg-MacLane 1942) that the collection of all mathematical structures of a given type, together with all the maps between them , is itself an instance of a nontrivial structure which can be studied in its own right. In keeping with this idea, the real objects of study are not so much categories themselves as the maps between themfunctors, natural transformations and (perhaps most important of all) adjunctions. Category theory has had great success in the unification of ideas from different areas of mathematics; it has now become an indispensable tool for anyone doing research in topology, abstract algebra, mathematical logic or theoretical computer science (to name but a few examples). This course aims to give a general introduction to category theory, without any (intentional!) bias in the direction of any particular application. It should therefore be of interest to a large proportion of pure Part III students. Categories, functors and natural transformations.
ISM Category Theory
category theory and Applications. Category Montreal has been an importantresearch centre in category theory for more than 20 years. The
http://www.math.uqam.ca/ISM/english/ecat.html

Extractions: Category Theory and Applications Category theory is a mathematical discipline that is characterized by its role in unifying mathematics as well as its foundational vocation. Since it was created by Eilenberg and MacLane, its influence has grown both in breadth and depth. The history of its development is intimately linked to that of contemporary mathematics. Montreal has been an important research centre in category theory for more than 20 years. The ISM offers a complete program of applications of category theory in the following areas: The program includes training in general category theory and in the history of contemporary mathematics. Topics in Algebra III : Covering toposes with singularities The title of this course paraphrases that of a landmark 1957 paper by R.H. Fox, "Covering spaces with singularities''. The course will be centered around the connection which exists between complete spreads (with a locally connected domain) over a topos and distributions on the topos, and with a related factorization theorem for geometric morphisms. After a brief selected introduction to topos theory we will discuss distributions, complete spreads, and the symmetric topos. Special topics will be selected from the following: branched coverings and knot groupoids, exponentiable complete spreads, admissible KZ-doctrines, single universes for functions and distributions, categories of cosheaves. Notes of a preliminary version of a book in preparation by Marta Bunge and Jonathon Funk will be distributed as a basis for the course.
Computational Category Theory At Macquarie
Computational category theory projects at Macquarie. Participants. TheInternational Computational category theory Project. This site
http://www.ics.mq.edu.au/~mike/compcat/

Extractions: Until this page is better developed you can get some idea of some of the work we do by looking at the following publications, most (but not all) of which relate to computational category theory and what we seek to do with the tools these projects are developing. This site is part of The Computational Category Theory Project Currently connected with this project are: Como, Italy Contact: R.F.C. Walters Walters@fis.unico.it University of North Wales, Bangor, Wales Contact: R. Brown
TUNES : Category Theory 101
category theory 101. A Learning Lounge course about category theory. Short introductioncategory theory entry on the Stanford Encyclopedia of Philosophy.
http://cliki.tunes.org/Category Theory 101

Extractions: CLiki pages can be edited by anybody at any time. Imagine a . Double it. Add two. [ Recent Changes ] [ About CLiki ] [ Text Formatting ] [ Create new page ] A Learning Lounge course about Category Theory The basics: A category is a thing with objects and arrows 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.
TUNES : Category Theory
category theory. See our category theory 101 overview. category theory is very usefulin formalizing types and functions/functors in functional programming.
http://cliki.tunes.org/category theory

Extractions: CLiki pages can be edited by anybody at any time. Imagine a . Double it. Add two. [ Recent Changes ] [ About CLiki ] [ Text Formatting ] [ Create new page ] 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. Page in this topic: Category Theory 101 Also linked from: Charity Monad Relational Show ... Search:
The Church Project: Study Group In Category Theory
Study Group in category theory. It was aimed at providing a insight into categorytheory for the working programming languages theory inclined person.
http://types.bu.edu/category.html

Extractions: The study group ran in the Fall 2000. It was aimed at providing a insight into category theory for the working programming languages theory inclined person. We intended on understanding the theory through examples on how category is applied within the field of programming languages. In the start of the most of the basic definitions were covered. In the fall we will read study examples on how category theory is applied in computer science: This is the list of the reading that we did. References are given using brackets, e.g. , and can be found in the bibliography below. Date Reading Theory Applications May 17 [Gold] : Chapter 1, 2, and 3.1-4 May 24 [Gold] : Chapter 3.5-9 May 31 [Gold] : Chapter 3.10-14 June 7 [Gold] : Chapter 3.15-16 Sep 26 Oct 3 Diagrams and natural transformations (4.1-4.3 of Oct 10
Re: SUO: Category Theory
Re SUO category theory. I also believe that category theory is theproper formalism to use for what the IFF is supposed to do.
http://suo.ieee.org/email/msg09004.html

Extractions: Thread Links Date Links Thread Prev Thread Next Thread Index Date Prev ... Date Index http://www.jfsowa.com/logic/math.htm John Sowa SUO: Re: Category Theory From: References SUO: Category Theory From: Prev by Date: SUO: Re: Category Theory Next by Date: SUO: Re: Category Theory Prev by thread: SUO: Re: Category Theory Next by thread: SUO: Re: Category Theory Index(es): Date Thread

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