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Sketches Of An Elephant A Topos Theory Compendium
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Book Synopsis Sketches of an Elephant: A Topos Theory Compendium by : P. T. Johnstone
Download or read book Sketches of an Elephant: A Topos Theory Compendium written by P. T. Johnstone and published by Oxford University Press. This book was released on 2002-09-12 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sketches of an Elephant by : Peter T. Johnstone
Download or read book Sketches of an Elephant written by Peter T. Johnstone and published by Clarendon Press. This book was released on 2002-06 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Now available in this two volume set, it contains all the important information both volumes provides. Considered to be a complete benefit for all researchers and academics in theoretical computer science, logicians and philosophers who study the foundations of mathematics, and those working in differential geometry and continuum physics.
Book Synopsis Sketches of an Elephant: A Topos Theory Compendium by : Peter T. Johnstone
Download or read book Sketches of an Elephant: A Topos Theory Compendium written by Peter T. Johnstone and published by Clarendon Press. This book was released on 2002-09-12 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topos Theory is an important branch of mathematical logic of interest to theoretical computer scientists, logicians and philosophers who study the foundations of mathematics, and to those working in differential geometry and continuum physics. This compendium contains material that was previously available only in specialist journals. This is likely to become the standard reference work for all those interested in the subject.
Book Synopsis Sketches of an Elephant: Toposes as categories ; 2-categorical aspects of topos theory by : P. T. Johnstone
Download or read book Sketches of an Elephant: Toposes as categories ; 2-categorical aspects of topos theory written by P. T. Johnstone and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Sketches of an Elephant: Toposes as spaces ; Toposes as theories by : P. T. Johnstone
Download or read book Sketches of an Elephant: Toposes as spaces ; Toposes as theories written by P. T. Johnstone and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Category Theory in Context by : Emily Riehl
Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Book Synopsis Interpolation and Definability by : Dov M. Gabbay
Download or read book Interpolation and Definability written by Dov M. Gabbay and published by Oxford University Press. This book was released on 2005-05-12 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.
Book Synopsis Category Theory And Applications: A Textbook For Beginners (Second Edition) by : Marco Grandis
Download or read book Category Theory And Applications: A Textbook For Beginners (Second Edition) written by Marco Grandis and published by World Scientific. This book was released on 2021-03-05 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Book Synopsis Computability and Randomness by : André Nies
Download or read book Computability and Randomness written by André Nies and published by OUP Oxford. This book was released on 2012-03-29 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.
Download or read book Set Theory written by John L. Bell and published by OUP Oxford. This book was released on 2011-05-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.
Download or read book Monoidal Topology written by Dirk Hofmann and published by Cambridge University Press. This book was released on 2014-07-31 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.
Book Synopsis Axiomatic Method and Category Theory by : Andrei Rodin
Download or read book Axiomatic Method and Category Theory written by Andrei Rodin and published by Springer Science & Business Media. This book was released on 2013-10-14 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Book Synopsis The Structure of Models of Peano Arithmetic by : Roman Kossak
Download or read book The Structure of Models of Peano Arithmetic written by Roman Kossak and published by Oxford University Press. This book was released on 2006-06-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, research logicians and mathematicians, this much-awaited text covers over 40 years of work on relative classification theory for nonstandard models of arithmetic. The book covers basic isomorphism invariants: families of type realized in a model, lattices of elementary substructures and automorphism groups.
Book Synopsis Concepts of Proof in Mathematics, Philosophy, and Computer Science by : Dieter Probst
Download or read book Concepts of Proof in Mathematics, Philosophy, and Computer Science written by Dieter Probst and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-25 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Book Synopsis From Sets and Types to Topology and Analysis by : Laura Crosilla
Download or read book From Sets and Types to Topology and Analysis written by Laura Crosilla and published by Oxford University Press. This book was released on 2005-10-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the foundations and practice of constructive mathematics, this text focusses on the contrast between the theoretical developments - which have been most useful for computer science - and more specific efforts on constructive analysis, algebra and topology.
Book Synopsis What is Category Theory? by : Giandomenico Sica
Download or read book What is Category Theory? written by Giandomenico Sica and published by Polimetrica s.a.s.. This book was released on 2006 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theories, Sites, Toposes by : Olivia Caramello
Download or read book Theories, Sites, Toposes written by Olivia Caramello and published by Oxford University Press. This book was released on 2018-01-19 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Grothendieck, the notion of topos is "the bed or deep river where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the continuous and that of discontinuous or discrete structures". It is what he had "conceived of most broad to perceive with finesse, by the same language rich of geometric resonances, an "essence" which is common to situations most distant from each other, coming from one region or another of the vast universe of mathematical things". The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision by building on the notion of classifying topos educed by categorical logicians. Mathematical theories (formalized within first-order logic) give rise to geometric objects called sites; the passage from sites to their associated toposes embodies the passage from the logical presentation of theories to their mathematical content, i.e. from syntax to semantics. The essential ambiguity given by the fact that any topos is associated in general with an infinite number of theories or different sites allows to study the relations between different theories, and hence the theories themselves, by using toposes as 'bridges' between these different presentations. The expression or calculation of invariants of toposes in terms of the theories associated with them or their sites of definition generates a great number of results and notions varying according to the different types of presentation, giving rise to a veritable mathematical morphogenesis.
