Book Description
Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one
stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient and natural solution to this problem by developing the notion of a frame relative to an elementary topos. The authors show how this technique enables a logical
approach to be taken to topics such as category theory relative to a topos and the relative Giraud theorem. The work is self-contained except that the authors presuppose a familiarity with basic category theory and topos theory. Logicians, set and category theorists, and computer scientist working
in the field will find this work essential reading. ... Read more

Book Description
The technique of diagrammatic morphisms is an importantingredient in comprehending and visualizing certain types ofcategories with structure. It was widely used in this capacityin many areas of algebra, low-dimensional topology and physics.It was also applied to problems in classical and quantuminformation processing and logic.

This volume contains articles based on talks at the SpecialSession, "Diagrammatic Morphisms in Algebra, Category Theory,and Topology", at the AMS Sectional Meeting in San Francisco.The articles describe recent achievements in several aspects ofdiagrammatic morphisms and their applications. Some of themcontain detailed expositions on various diagrammatic techniques.The introductory article by D. Yetter is a thorough account ofthe subject in a historical perspective. ... Read more

Book Description
This digital document is an article from The Review of Metaphysics, published by Philosophy Education Society, Inc. on September 1, 2001. The length of the article is 1041 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Aristotle's Theory of Substance: The Categories and Metaphysics Zeta. (book review)
Author: Michael Golluber
Publication: The Review of Metaphysics (Refereed)
Date: September 1, 2001
Publisher: Philosophy Education Society, Inc.
Volume: 55Issue: 1Page: 167(3)

Article Type: Book Review

Distributed by Thomson Gale ... Read more

Book Description
This book reviews recent results on low-dimensional quantum field theoriesand their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematicallyprecise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of therepresentation theory of U (sl ), for q a primitive root of unity, and asemi-simple quotient thereof, a classfication of braided tensor categoriesgenerated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum fieldtheory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students. ... Read more

Book Description
As category theory approaches its first half-century, itcontinues to grow, finding new applications in areas that wouldhave seemed inconceivable a generation ago, as well as in moretraditional areas. The language, ideas, and techniques ofcategory theory are well suited to discovering unifyingstructures in apparently different contexts. Representing thisdiversity of the field, this book contains the proceedings of aninternational conference on category theory. The subjectscovered here range from topology and geometry to logic andtheoretical computer science, from homotopy to braids andconformal field theory. Although generally aimed at experts inthe various fields represented, the book will also provide anexcellent opportunity for nonexperts to get a feel for thediversity of current applications of category theory. ... Read more

Book Description
This edited volume gives an overview of the concepts andmethods used in current research in quantum logic, viewed both as anoperational physical theory and in terms of purely mathematicalstructure. Far from being simply a collation of research papers, itconsists of 11 specially commissioned essays that, taken together,provide both an introduction to quantum logic and an overview ofcurrent research in this subject. The contributors, who include someof the most distinguished names in the field, discuss topics rangingfrom the algebraic theory of orthomodular lattices to recentapplications of category-theoretic methods and connections withtheoretical computer science. Moreover, an historical overview of thefield and an extensive citation and concept index are included.
Audience: This volume, dedicated to D.J. Foulis in honour of hisseminal contributions to quantum logic, should interest puremathematicians, theoretical physicists, computer scientists andphilosophers of science. ... Read more

Book Description
This digital document is a journal article from Mathematical Social Sciences, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
A decision making problem is considered from algebraic point of view. The set of outcomes (consequences) is supposed to be partially ordered according to the decision maker's preferences. The problem is how these preferences affect a decision maker to prefer one of his strategies (or acts) over another, i.e., to describe suitable preference relations (called derived preference relations) on the set of the decision maker's strategies. This problem is formalized by using a category theory approach and is reduced to a pure algebraical question. An effective method is suggested for constructing all reasonable derived preference relations and some examples are presented which illustrate how the method is applied. ... Read more

Book Description
Mathematicians interested in understanding the directions ofcurrent research in set theory will not want to overlook thisbook, which contains the proceedings of the AMS Summer ResearchConference on Axiomatic Set Theory, held in Boulder, Colorado,June 19--25, 1983. This was the first large meeting devotedexclusively to set theory since the legendary 1967 UCLA meeting,and a large majority of the most active research mathematiciansin the field participated. All areas of set theory, includingconstructibility, forcing, combinatorics and descriptive settheory, were represented; many of the papers in the proceedingsexplore connections between areas. Readers should have abackground of graduate-level set theory.

There is a paper by S.~Shelah applying proper forcing to obtainconsistency results on combinatorial cardinal "invariants" belowthe continuum, and papers by R.~David and S.~Freidman onproperties of $0^\#$. Papers by A.~Blass, H.-D.~Donder, T.~Jechand W.~Mitchell involve inner models with measurable cardinalsand various combinatorial properties. T.~Carlson largely solvesthe pin-up problem, and D.~Velleman presents a novelconstruction of a Souslin tree from a morass. S.~Todorcevicobtains the strong failure of the \qedprinciple from the ProperForcing Axiom and A.~Miller discusses properties of a newspecies of perfect-set forcing. H.~Becker and A.~Kechris attackthe third Victoria Delfino problem while W.~Zwicker looks atcombinatorics on $P_\kappa(\lambda)$ and J.~Henle studiesinfinite-exponent partition relations. A.~Blass shows that ifevery vector space has a basis then $AC$ holds. I.~Anellistreats the history of set theory, and W.~Fleissner presentsset-theoretical axioms of use in general topology. ... Read more