Categorical Geometry

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Categorical Theory: Categories, Types and Structures: an introduction to Category Theory for the working computer scientist. (PostScript) by Andrea Asperti and Giuseppe Longo, M.I.T.- Press, 1991. (pp. 1--300). (Available by ftp, see the book content page in Downloadable Papers). Basic Category Theory (AbstractPostScriptDVI)  (a publication in Basic Research in Computer Science) by Jaap van Oosten, January 1995. vi+75 pp.  Algebra: Abstract Algebra On Line A Site maintained by John Beachy Finite Rank Torsion Free Modules Over Dedekind Domains A Book by Lee Lady Algebraic Geometry Algebraic Geometry Seminar Algebraic Geometry A Book. by J.S.Milne History of Mathematics: History of Mathematics archive at the School of Mathematics, Trinity College, Dublin. Biographies of some seventeenth and eighteenth century mathematicians, taken from A short account of the history of mathematics (4th edition, 1908) by W. W. Rouse Ball. Mathematical papers and other material relating to certain mathematicians and philosophers, including Hamilton,  Berkeley, Boole, Riemann, Cantor and Newton. A directory of Web sites and pages around the world relevant to the history of mathematics.  Hermann Grassmann and the Prehistory of Universal Algebra Hermann Grassmann and the Creation of Linear Algebra by  Desmond Fearnley-Sander Research Bibliography: CATEGORY THEORY General Interests: Stanford Encyclopedia of Philosophy  (Table of Contents)

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Category Theory

Abstract and Concrete Categories :  The Joy of Cats Jiri Adamek (Contributor), et al  Paperback 1990 List: $127.00 (Special Order) Buy It Online at amazon.com Reviews A modern introduction to the theory of structures via the language of category theory. Unique to this book is the emphasis on concrete categories. Also noteworthy is the systematic treatment of factorization structures, which gives a new, unifying perspective to earlier work and summarizes recent developments. Each categorical notion is accompanied by many examples, usually moving from special cases to more general cases. Comprises seven chapters; the first five present the basic theory, while the last two contain more recent research results in the realm of concrete categories, cartesian closed categories and quasitopoi. The prerequisite is an elementary knowledge of set theory. Contains exercises.

Handbook of Categorical Algebra 1 : Basic Category Theory (Encyclopedia of Mathematics and Its Applications, Vol 50) Francis Borceux Hardcover 1994  List: $80.00 Buy It Online at amazon.com Reviews The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.

Handbook of Categorical Algebra 2 :  Categories and Structures  (Encyclopedia of Mathematics and Its Applications, Vol 51) Francis Borceux Hardcover 1994 List: $90.00 (Special Order) Buy It Online at amazon.com Reviews The second volume, which assumes familiarity with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and applications. In addition, after several chapters discussing specific categories, the book develops all the major concepts concerning Benabou's ideas of fibered categories.

Categories for the Working Mathematician (2nd Ed) (Graduate Texts in Mathematics, 5) Saunders Mac Lane, et al Hardcover 1988 List: $54.95 Buy It Online at amazon.com Reviews Categories for the Working Mathematician provides an array of general ideas useful in a wide variety  of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural  transformation, and duality. The book then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterized by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions.

Conceptual Mathematics :  A First Introduction to Categories F. William Lawvere, et al  Hardcover 1997  List: $90.00 Buy It Online at amazon.com Reviews The idea of a "category"--a sort of mathematical universe--has brought about a remarkable unification and simplification of mathematics. Written by two of the best known names in categorical logic, this is the first book to apply categories to the most elementary mathematics.

Categorical Geometry

Categories of Commutative Algebras Yves Diers Hardcover 1992 List: $79.00 Buy It Online at amazon.com Reviews A study of the properties and structures of categories of commutative algebras in order to bring out universal properties of these categories and provide a universal framework for commutative algebra and algebraic geometry. The aim is to extend the domain of validity and application of the large number of results obtained.

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