Toposes Triples And Theories
DOWNLOAD
Download Toposes Triples And Theories PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Toposes Triples And Theories book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Toposes Triples And Theories
DOWNLOAD
Author : M. Barr
language : en
Publisher: Springer
Release Date : 2013-06-09
Toposes Triples And Theories written by M. Barr and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-09 with Mathematics categories.
As its title suggests, this book is an introduction to three ideas and the connections between them. Before describing the content of the book in detail, we describe each concept briefly. More extensive introductory descriptions of each concept are in the introductions and notes to Chapters 2, 3 and 4. A topos is a special kind of category defined by axioms saying roughly that certain constructions one can make with sets can be done in the category. In that sense, a topos is a generalized set theory. However, it originated with Grothendieck and Giraud as an abstraction of the of the category of sheaves of sets on a topological space. Later, properties Lawvere and Tierney introduced a more general id~a which they called "elementary topos" (because their axioms did not quantify over sets), and they and other mathematicians developed the idea that a theory in the sense of mathematical logic can be regarded as a topos, perhaps after a process of completion. The concept of triple originated (under the name "standard construc in Godement's book on sheaf theory for the purpose of computing tions") sheaf cohomology. Then Peter Huber discovered that triples capture much of the information of adjoint pairs. Later Linton discovered that triples gave an equivalent approach to Lawverc's theory of equational theories (or rather the infinite generalizations of that theory). Finally, triples have turned out to be a very important tool for deriving various properties of toposes.
Toposes Triples And Theories
DOWNLOAD
Author : Michael Barr
language : en
Publisher:
Release Date : 2002
Toposes Triples And Theories written by Michael Barr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Toposes And Local Set Theories
DOWNLOAD
Author : John L. Bell
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Toposes And Local Set Theories written by John L. Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Topos Theory
DOWNLOAD
Author : P.T. Johnstone
language : en
Publisher: Courier Corporation
Release Date : 2014-01-15
Topos Theory written by P.T. Johnstone and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with Mathematics categories.
Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.
Sketches Of An Elephant
DOWNLOAD
Author : Peter T. Johnstone
language : en
Publisher: Oxford University Press
Release Date : 2002
Sketches Of An Elephant written by Peter T. Johnstone and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Toposes categories.
Generalized Etale Cohomology Theories
DOWNLOAD
Author : John Jardine
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-15
Generalized Etale Cohomology Theories written by John Jardine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-15 with Mathematics categories.
A generalized etale cohomology theory is a theory which is represented by a presheaf of spectra on an etale site for an algebraic variety, in analogy with the way an ordinary spectrum represents a cohomology theory for spaces. Examples include etale cohomology and etale K-theory. This book gives new and complete proofs of both Thomason's descent theorem for Bott periodic K-theory and the Nisnevich descent theorem. In doing so, it exposes most of the major ideas of the homotopy theory of presheaves of spectra, and generalized etale homology theories in particular. The treatment includes, for the purpose of adequately dealing with cup product structures, a development of stable homotopy theory for n-fold spectra, which is then promoted to the level of presheaves of n-fold spectra. This book should be of interest to all researchers working in fields related to algebraic K-theory. The techniques presented here are essentially combinatorial, and hence algebraic. An extensive background in traditional stable homotopy theory is not assumed. ------ Reviews (...) in developing the techniques of the subject, introduces the reader to the stable homotopy category of simplicial presheaves. (...) This book provides the user with the first complete account which is sensitive enough to be compatible with the sort of closed model category necessary in K-theory applications (...). As an application of the techniques the author gives proofs of the descent theorems of R. W. Thomason and Y. A. Nisnevich. (...) The book concludes with a discussion of the Lichtenbaum-Quillen conjecture (an approximation to Thomason’s theorem without Bott periodicity). The recent proof of this conjecture, by V. Voevodsky, (...) makes this volume compulsory reading for all who want to be au fait with current trends in algebraic K-theory! - Zentralblatt MATH The presentation of these topics is highly original. The book will be very useful for any researcher interested in subjects related to algebraic K-theory. - Matematica
Algebraic Theories
DOWNLOAD
Author : J. Adámek
language : en
Publisher: Cambridge University Press
Release Date : 2010-11-18
Algebraic Theories written by J. Adámek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-18 with Mathematics categories.
Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.
Fundamentals Of Computation Theory
DOWNLOAD
Author : Gabriel Ciobanu
language : en
Publisher: Springer
Release Date : 2003-07-31
Fundamentals Of Computation Theory written by Gabriel Ciobanu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Computers categories.
This book constitutes the refereed proceedings of the 12th International Symposium on Fundamentals of Computation Theory, FCT '99, held in Iasi, Romania in August/September 1999. The 42 revised full papers presented together with four invited papers were carefully selected from a total of 102 submissions. Among the topics addressed are abstract data types, algorithms and data structures, automata and formal languages, categorical and topological approaches, complexity, computational geometry, concurrency, cryptology, distributed computing, logics in computer science, process algebras, symbolic computation, molecular computing, quantum computing, etc.
Elementary Categories Elementary Toposes
DOWNLOAD
Author : Colin McLarty
language : en
Publisher: Clarendon Press
Release Date : 1992-06-04
Elementary Categories Elementary Toposes written by Colin McLarty and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-04 with categories.
The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -
Topoi
DOWNLOAD
Author : Robert Goldblatt
language : en
Publisher: Courier Corporation
Release Date : 2013-07-25
Topoi written by Robert Goldblatt and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-25 with Mathematics categories.
A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers.