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Category Theory:     more books (100)

Category Theory (Oxford Logic Guides) by Steve Awodey, 2010-08-13 Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce, 1991-08-07 Basic Concepts of Enriched Category Theory (London Mathematical Society Lecture Note Series) by Max Kelly, 1982-04-30 Sets, Logic and Categories (Springer Undergraduate Mathematics Series) by Peter J. Cameron, 1999-03-05 Categories for the Working Mathematician (Graduate Texts in Mathematics) by Saunders Mac Lane, 1998-09-25 What is Category Theory? Abstract and Concrete Categories: The Joy of Cats (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) by Jiri Adamek, Horst Herrlich, et all 1990-04 Formal Category Theory : Adjointness for 2-Categories (Lecture Notes in Mathematics) (Volume 0) by J.W. Gray, 1974-08-20 Evolutionary Metaphysics: The Development of Peirce's Theory of Categories by Joseph L. Esposito, 1980-12 Aristotle's Theory of Substance: The Categories and Metaphysics Zeta (Oxford Aristotle Studies) by Michael V. Wedin, 2002-12-12 From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory (Logic, Epistemology, and the Unity of Science) by Jean-Pierre Marquis, 2008-12-05 Categories and Sheaves (Grundlehren der mathematischen Wissenschaften) by Masaki Kashiwara, Pierre Schapira, 2009-12-15 Divisor Theory by Harold M. Edwards, 1990-01-01 Categorical Logic and Type Theory, Volume 141 (Studies in Logic and the Foundations of Mathematics) by B. Jacobs, 2001-05-24

lists with details

1. Category Theory
   This expository article is an entry in the Stanford Encyclopedia of Philosophy.  
   http://plato.stanford.edu/entries/category-theory/
   
   Extractions: FEB defined as sets, category theory cannot provide a philosophically enlightening foundation for mathematics. In terms of collections, 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 Mor a b ), namely, the morphisms from a to b in C (when f is a morphism from a to b , we write f a b For every triple a b and c of objects, there is a partial operation from pairs of morphisms in Mor a b ) X Mor b c ) to morphisms in Mor a c ), called the composition of morphisms in C

2. CT Category Theory
   Section of the eprint arXiv dealing with category theory, including such topics as enriched categories, topoi, abelian categories, monoidal categories, homological algebra.  
   http://front.math.ucdavis.edu/math.CT
   
   Extractions: Authors: AB CDE FGH IJK ... U-Z 3 Jun math.GR/0406044 On the Zappa-Szep Product. Matthew G. Brin . 29 pages. GR CT 28 May math.QA/0405517 Fiber Functors on Temperley-Lieb Categories. Yamagami Shigeru . 19 pages. QA CT 25 May math.AG/0405453 Michel Hickel . 45 pages. AG CT 13 May math.KT/0405227 Hochschild cohomology of abelian categories and ringed spaces. W. T. Lowen , M. Van den Bergh . 38 pages. KT CT 30 Apr math.RA/0404522 Algebra generators and information theory. T. Kopf , R. Otahalova . 5 pages. RA CT 29 Apr math.QA/0404504 An analogue of Radford's S^4 formula for finite tensor categories. Pavel Etingof , Dmitri Nikshych , Viktor Ostrik . 14 pages. QA CT 28 Apr math.AT/0404470

3. Introduction To Category Theory
   A Gentle Introduction to category theory the calculational approach. Maarten M Fokkinga 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

4. 18: Category Theory, Homological Algebra
   category theory, a comparatively new field of mathematics, provides a universal framework for discussing full, wideranging text on category theory is by Borceux, Francis "Handbook  
   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. A survey article which discusses the roles of categories and topoi in twentieth-century mathematics. 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.

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

6. Structuralism, Category Theory And Philosophy Of Mathematics
   By Richard Stefanik (Washington MSG Press,1994).  
   http://www.mmsysgrp.com/strctcat.htm

7. MATHS: Category Theory
   category theory. Motivation. category theory is a way for talking about the relationships between the classes computer science has found that category theory allowed them to express a  
   http://www.csci.csusb.edu/dick/maths/math_25_Categories.html
   
   Extractions: CSUSB CNS Comp Sci Dept R J Botting ... Comment ] Fri Feb 20 12:05:34 PST 2004 Category Theory is a way for talking about the relationships between the classes of objects modeled by mathematics and logic. It is a model of a collection of things with some structural similarity. It is a comparatively recent abstraction from the various abstract algebras developed in the early part of the 20th century. The best source for detailed information is still Madc Lane's classic graduate text The original use of the term category was in the idea of a 'categorical' axiom system - an axiom system which defined its objects so exactly that all objects that satisfied the axioms were isomorphic - they mapped into each other, one-to-one, preserving all the axioms and structure. This is important, because if a logic is categorical and there exists a simple (or cheaply implemented) example then that model can become the standard and all others are handled in terms of this standard. For example binary numbers have all the properties that one can expect of objects that satisfy the rules that describe a "natural number" and are cheap to emulate using electronics. The name for such ideal systems has been changed several times in this century - categorical, free, universal, initial,... Many times category theorists have discovered that some results that they have uncovered have been discovered within a totally different area - say the theory of languages and automata. Equally often an enterprising researcher in mathematics of computer science has found that category theory allowed them to express a specific property they had observed in more general terms. The more general veiw then leads to shorter and simpler proofs of more results. This in turn often illuminates other problems.

8. Applications Of Category Theory To Computer Science
   Workshop Applications of category theory to Computer Science. June 812, 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

9. Categories Home Page
   The Centre of Australian category theory (CoACT) based at Macquarie University has a page at http//www a postal mailing list (not updated) for category theory. At York University  
   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/

10. Comcat
    The aim of the project is the development of software on a wide variety of platforms for computing  
    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.

11. Categories
    In fact, MacLane said "I did not invent category theory to talk about functors go to objects and morphisms go to morphisms. 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

12. Computational Category Category Theory Project
    Computational category theory Project. Goals and Method. The aim of 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

13. Centre De Recherche En Théorie Des Catégories -- Montréal
    Centre de Recherche en Théorie des Catégories Montréal category theory Research Center. Translation? Some upcoming meetings. What is category theory?  
    http://www.math.mcgill.ca/triples/
    
    Extractions: Category Theory Research Center Translation? Some upcoming meetings 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 and more 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)

14. School On Category Theory And Applications
    SCHOOL ON category theory AND APPLICATIONS. This school is being organized by the category theory Group of the University of Coimbra.  
    http://www.mat.uc.pt/~scta/

15. Categories Home Page
    The following sites include links to general information on category theory, including much not found on this page Descent and category theory Connections  
    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/

16. Applied And Computational Category Theory
    A brief description of category theory, and some useful links.  
    http://www.risc.uni-linz.ac.at/research/category/

17. Category Theory - Wikipedia, The Free Encyclopedia
    category theory is a mathematical theory that deals in an abstract way with mathematical broadlybased foundational applications of category theory are contentious; but they have  
    http://www.wikipedia.org/wiki/Category_theory
    
    Extractions: edit 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

18. Category Theory - Wikipedia, The Free Encyclopedia
    category theory. category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them.  
    http://en.wikipedia.org/wiki/Category_theory
    
    Extractions: edit 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

19. Alex Simpson: Home Page
    University of Edinburgh category theory, domain theory, logic, type theory.  
    http://www.dcs.ed.ac.uk/~als/

20. Theory And Applications Of Categories
    Theory and Applications of Categories. ISSN 1201 561X. 3. Operads in higher-dimensional category theory Tom Leinster, 73-194 abstract dvi ps pdf.  
    http://www.tac.mta.ca/tac/

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