Elementary Categories Elementary Toposes
DOWNLOAD
Download Elementary Categories Elementary Toposes PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Elementary Categories Elementary Toposes 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
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. -
Model Theory And Topoi
DOWNLOAD
Author : F.W. Lawvere
language : en
Publisher: Springer
Release Date : 2006-11-15
Model Theory And Topoi written by F.W. Lawvere and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
A Collection of Lectures by Variuos Authors
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.
Topoi
DOWNLOAD
Author : R. Goldblatt
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Topoi written by R. Goldblatt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.
Sketches Of An Elephant A Topos Theory Compendium
DOWNLOAD
Author : P. T. Johnstone
language : en
Publisher: Oxford University Press
Release Date : 2002-09-12
Sketches Of An Elephant A Topos Theory Compendium written by P. 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 2002-09-12 with Computers categories.
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.
Sheaves In Geometry And Logic
DOWNLOAD
Author : Saunders Mac Lane
language : en
Publisher:
Release Date : 1992
Sheaves In Geometry And Logic written by Saunders Mac Lane and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Algebraische Geometrie - Garbentheorie categories.
An introduction to the theory of toposes which begins with illustrative examples and goes on to explain the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.
Conceptual Mathematics
DOWNLOAD
Author : F. William Lawvere
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-30
Conceptual Mathematics written by F. William Lawvere 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 2009-07-30 with Mathematics categories.
This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
Categorical Logic And Type Theory
DOWNLOAD
Author : B. Jacobs
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-05-10
Categorical Logic And Type Theory written by B. Jacobs and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-10 with Computers categories.
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
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.
Generic Figures And Their Glueings
DOWNLOAD
Author : Marie La Palme Reyes
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2004
Generic Figures And Their Glueings written by Marie La Palme Reyes and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.