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Topic: List of category theory topics

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	Encyclopedia: Category theory (Site not responding. Last check: 2007-10-21)
		One of the central themes of algebraic geometry is the equivalence of the category C of affine schemes and the category D of commutative rings.
		In category theory and its applications to other branches of mathematics, a kernel is a type of limit that generalises the notion of kernel from algebra in certain contexts.
		That is, the kernel of a morphism is its cokernel in the opposite category, and vice versa.
	www.nationmaster.com /encyclopedia/category-theory (521 words)

	Category theory - Wikipedia, the free encyclopedia
		Categories, functors and natural transformations were introduced by Samuel Eilenberg and Saunders Mac Lane in 1945.
		The subsequent development of the theory was powered first by the computational needs of homological algebra; and then by the axiomatic needs of algebraic geometry, the field most resistant to the Russell-Whitehead view of united foundations.
		These broadly-based foundational applications of category theory are contentious; but they have been worked out in quite some detail, as a commentary on or basis for constructive mathematics.
	en.wikipedia.org /wiki/Category_theory (2335 words)

	Category theory
		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.
		General category theory - an updated universal algebra with many new features allowing for semantic flexibility and higher-order logic - came later; it is now applied throughout mathematics.
		Any directed graph generates a small category: the objects are the vertices of the graph and the morphisms are the paths in the graph.
	pedia.newsfilter.co.uk /wikipedia/c/ca/category_theory.html (2305 words)

	Read about Category theory at WorldVillage Encyclopedia. Research Category theory and learn about Category theory here! (Site not responding. Last check: 2007-10-21)
		categories is an attempt to capture what is commonly found in various classes of related mathematical structures.
		A category is an axiomatic formulation of this idea of relating mathematical structures to the structure-preserving processes between them.
		By studying categories and functors, we are not just studying a class of mathematical structures and the morphisms between them, we are studying the relationships between various classes of mathematical structure.
	encyclopedia.worldvillage.com /s/b/Category_theory (2293 words)

	Category theory (Site not responding. Last check: 2007-10-21)
		Dual vectorspace: an example of a contravariant functor from the category of all real vector spaces to the category of all real vector spaces is given by assigning to every vector space its dual space and to every linear map its dual or transpose.
		Algebra of continuous functions: a contravariant functor from the category of topological spaces (with continuous maps as morphisms) to the category of real associative algebras is given by assigning to every topological space X the algebra C(X) of all real-valued continuous functions on that space.
		One may check that the map from the category of topological spaces with a distinguished point to the category of groups is functorial: a topological (homo/iso)morphism will naturally correspond to a group (homo/iso)morphism.
	www.sciencedaily.com /encyclopedia/category_theory (3261 words)

	Lists of articles by category : List of topics lists (Site not responding. Last check: 2007-10-21)
		None of these are yet comprehensive or up-to-date, but filling in or creating these lists will create an easy way to track articles by their categories, as well as creating an implicit to-do list of topics for which articles have not yet been written.
		Since these categories span broad disciplines of knowledge, these lists complement those found on the list of reference tables, which cover very narrow, specific topics.
		List of anomalous phenomenon (paranormal) and parapsychology topics
	www.explainthis.info /li/list-of-topics-lists.html (474 words)

	18: Category theory, homological algebra
		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.
		A full, wide-ranging text on category theory is by Borceux, Francis: "Handbook of categorical algebra", 3 vol (1: Basic category theory; 2: Categories and structures; 3: Categories of sheaves) (Encyclopedia of Mathematics and its Applications, 50-2.) Cambridge University Press, Cambridge, 1994.
	www.math.niu.edu /~rusin/known-math/index/18-XX.html (286 words)

	Categories Home Page
		Category Theory 2000 The international summer conference in category theory was held at Villa Olmo, Como, Italy from Sunday 16th July to Saturday 22nd July 2000.
		Category Theory Symposium The symposium was a special session of the Canadian Mathematical Society Summer 1998 Meeting June 13-15, 1998 at University of New Brunswick (Saint John) Saint John, New Brunswick, Canada and was part of a larger programme including plenary talks, one of which was given by S. Schanuel (SUNY Buffalo).
		Category Theory at the Isle of Thorns was held from July 7 to 12, 1996.
	www.mta.ca /~cat-dist/categories.html (3545 words)

	Conference: Category Theory and Computer Science (CTCS) (Site not responding. Last check: 2007-10-21)
		The purpose of the conference series is the advancement of the foundations of computing using the tools of category theory, algebra, geometry and logic.
		Whilst the emphasis is upon applications of category theory, it is recognised that the area is highly interdisciplinary and the organising committee welcomes submissions in related areas.
		Topics central to the conference include: Models of computation Program logics and specification Type theory and its semantics Domain theory Linear logic and its applications Categorical programming Submissions purely on category theory are also acceptable as long as the applicability to computing is evident.
	www.cis.upenn.edu /~bcpierce/types/archives/1994/msg00088.html (336 words)

	Category Theory - The Science Beat ... Scientific Research, Space, NASA - SearchBeat.com (Site not responding. Last check: 2007-10-21)
		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.
	www.searchbeat.com /Science/Math/Algebra/CategoryTheory (332 words)

	Encyclopedia: Abelian group (Site not responding. Last check: 2007-10-21)
		Previous to this work, groups were mainly studied concretely, in the form of permutations; some aspects of abelian group theory were known in the theory of quadratic forms.
		A group that we are introduced to in elementary school is the integers under addition.
		Given a group G and a normal subgroup N, the quotient group is the set of cosets of G/N together with the operation (gN)(hN)=ghN.
	www.nationmaster.com /encyclopedia/Abelian-group (378 words)

	COMPOSITIONS
		As a matter of history, the category concept was introduced in algebraic topology, as an important part of the transition from homology (an intuitive and geometric concept) to homology theory, an axiomatic approach.
		Broadly-based foundational applications of category theory are contentious; but they have been worked out in quite some detail, as a commentary on or basis for constructive mathematics.
		Category theory is also used in a foundational way in functional programming, for example to discuss the idea of typed lambda calculus in terms of cartesian closed categories.
	www.websters-online-dictionary.org /definition/COMPOSITIONS (5521 words)

	The Math Forum - Math Library - Cat. Theory/Homolgcl Alg. (Site not responding. Last check: 2007-10-21)
		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.
		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.
		A set of tools for computation in the category of combinatorial sheaves, intended for research involving complexes of sheaves and the derived category.
	mathforum.org /library/topics/category_theory (769 words)

	My current readings in Category Theory
		Cypherpunks, I've been having a lot of fun reading up on "category theory," a relatively new branch of math that offers a unified language for talking about (and proving theorems about) the transformations between objects.
		The basic insight is that just as category theory is about "objects/things" (called categories) and the "transformations/functions" (called arrows) between them, this is what a lot of crypto protocols are.
		And in areas closely-related to many Cypherpunks topics, I can think of several examples where overly-broad claims have been made for some theory or paradigm and how it solves many problems: * "general semantics," the Korzybski work which led to "the map is not the territory." Much-quoted by SF authors like Heinlein.
	www.mail-archive.com /cypherpunks-moderated%40minder.net/msg00145.html (1823 words)

	GDCT: Java Source Files [Complete]
		It displays a list of objects in categories that are presently in memory.
		The user can select a category from a choice menu and then changes made to the category to make it confluent will be displayed in the text area.
		This class displays a frame which allows the user to change the default server, default server category directory, and the default server functor directory, which are used in the loading of files.
	mathcs.mta.ca /research/rosebrugh/gdct/javasource.htm (2139 words)

	Directory Plug - Science Math Algebra Category Theory - Free Directory Listings (Site not responding. Last check: 2007-10-21)
		In theory, the hydrogen had been deposited there by solar winds and, if harnessed, could be used by astronauts as an energy source.Though the project ne...
		Computational Category Theory - An implementation of concepts and constructions from category theory in the functional programming language Standard ML.
		CT Category Theory - Section of the e-print arXiv dealing with category theory, including such topics as: enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
	www.rovisoft.com /Science/Math/Algebra/Category_Theory (631 words)

	List of group theory topics - Wikipedia, the free encyclopedia
		See also: List of abstract algebra topics, List of category theory topics, list of Lie group topics.
		See also list of harmonic analysis and representation theory topics
		This page was last modified 05:31, 13 January 2006.
	www.wikipedia.org /wiki/List_of_group_theory_topics (184 words)

	Some books on category and topos theory
		The authors are pioneers in topos theory, but the presentation is suitable for any bright person.
		A topos is a kind of generalization of the universe of set theory that we all know and love, but topos theory is really a wonderful way to unify and generalize vast swathes of mathematics - you could say it's the way that logic and topology merge when you take category theory seriously.
		I'm here now, in my one and only present, and this category and topos theory is turning out to be enjoyable and stimulating as a goal unto itself, and as a tool for, I think, better understanding things I want to understand.
	www.mail-archive.com /everything-list@eskimo.com/msg03705.html (1243 words)

	Category:Number theory - (Site not responding. Last check: 2007-10-21)
		Traditionally, number theory mathematics concerned with the properties of integers and many open problems that are easily understood even by non-mathematicians.
		Number theory may be subdivided into several fields according to the methods used and the questions investigated.
		See for example the list of number theory topics.
	www.grohol.com /psypsych/Category:Number_theory (199 words)

	Conference on CATEGORY THEORY AND COMPUTER SCIENCE (Site not responding. Last check: 2007-10-21)
		Date: Wed, 2 May 90 22:58:13 +0200 CATEGORY THEORY AND COMPUTER SCIENCE (first announcement and call for papers) 3-6 September 1991 Ecole Normale Superieure, Paris The Fourth of the biennial Summer Conferences on Category Theory and Computer Science will be held in Paris.
		The main purpose of these conferences is to link research in category theory with computer science.
		The importance of categories in understanding basic issues in computer science is now well established.
	www.cis.upenn.edu /~bcpierce/types/archives/1990/msg00026.html (181 words)

	Amazon.com: Basic Category Theory for Computer Scientists (Foundations of Computing): Books: Benjamin C. Pierce (Site not responding. Last check: 2007-10-21)
		Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse.
		Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations.
		If you would like to know the first step of Category Theory and you are in CS realm, this book is the one you have to try.
	www.amazon.com /exec/obidos/tg/detail/-/0262660717 (1209 words)

	Topics: Category Theory (Site not responding. Last check: 2007-10-21)
		Equivalently: A category can be defined as a directed network with an associative composition and identities: Hom(X,Y) are the edges from X to Y.
		Def: An element f in Hom(X,Y), where X and Y are some elements of a category A.
		Automorphism: A bijective endomorphism of an object in a category (onto itself) f: G → G; an inner one is one that is generated by a g in G, and the map f: G → G can be written a
	www.phy.olemiss.edu /~luca/Topics/c/category.html (549 words)

	Algebra / Category Theory (Site not responding. Last check: 2007-10-21)
		Section of the e-print arXiv dealing with category theory, including such topics as: enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
		An implementation of concepts and constructions from category theory in the functional programming language Standard ML.
		Categories appear in most branches of mathematics, in some areas of theoretical computer...
	paloweb.com /Science/Math/Algebra/Category_Theory (449 words)

	Savage Minds: Notes and Queries in Anthropology — A Group Blog » Theory
		And done well the courses are too—they have a PDF brochure with more course listings (including readings and a rough schedule) and there is additional information and readings in short pieces in Critical Quarterly 42(2)—a description of the logic behind the classes and a list (both require authentication—sorry).
		While I don’t deny that theories have a moral and ethical component, I think Flyvbjerg is too quick to give up attempts at creating explanations of society altogether.
		Dustin: I don't think John was saying "theory in anthropology" is crap, but that the currently-existing state of anthropology...
	savageminds.org /category/theory (5873 words)

	Basic Category Theory for Computer Scientists (Foundations of Computing) - shop at talkhd.tv (Site not responding. Last check: 2007-10-21)
		The first 50 pages are about general category theory, and the last 20 pages are specifically for computer scientists.
		My interest is in general category theory, and I bought this because I have a BS in CS and thought I'd find plenty of familiar examples.
		The case studies at the end put everything into context and prepare you for CS texts on semantics, type theory, etc.
	www.talkhd.tv /amazon/asinsearch_0262660717.html (287 words)

	Category Theory (Site not responding. Last check: 2007-10-21)
		This is a huge field: I am not interested in categories as a foundational theory, preferring von Neumann-Gödel-Bernays class/set theory instead, but some topics are fascinating.
		The Sydney categories group[FTP] has papers and software by members of the group, plus a mailing list for Category Theory.
		This is an introduction to sheave-theoretic techniques in logic, pointed toward the proof of Cohen's result on the independence of the continuum hypothesis from the other axioms of set theory with categorical means; well written and easy to understand, with a lot of examples.
	www.math.unifi.it /~caressa/math/catego.html (214 words)

	Amazon.co.uk: Topology and Category Theory in Computer Science: Books (Site not responding. Last check: 2007-10-21)
		Since techniques from topology and category theory have been used increasingly by theoretical computer scientists in recent years, it was decided to hold a special session at the symposium which would be devoted to the application of these topics in computer science.
		All those who had presented papers, plus a very few others, were invited to submit papers for these proceedings of the special session on topology and category theory in computer science.
		By holding this session in the context of the topology symposium, the organisers hoped to achieve a cross-fertilization between the communities they brought together - giving one a course of new problems with a more practical flavour, and the other a source of solutions and ideas.
	www.amazon.co.uk /exec/obidos/ASIN/0198537603 (555 words)

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