Sketches Of An Elephant A Topos Theory Compendium
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| Author | : P. T. Johnstone |
| Publisher | : Oxford University Press |
| Total Pages | : 836 |
| Release | : 2002-09-12 |
| Genre | : Computers |
| ISBN | : 9780198515982 |
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.
| Author | : Peter T. Johnstone |
| Publisher | : Clarendon Press |
| Total Pages | : 880 |
| Release | : 2002-06 |
| Genre | : Toposes |
| ISBN | : 9780199611386 |
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.
| Author | : Dov M. Gabbay |
| Publisher | : Oxford University Press |
| Total Pages | : 524 |
| Release | : 2005-05-12 |
| Genre | : Computers |
| ISBN | : 0198511744 |
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.
| Author | : Emily Riehl |
| Publisher | : Courier Dover Publications |
| Total Pages | : 273 |
| Release | : 2017-03-09 |
| Genre | : Mathematics |
| ISBN | : 0486820807 |
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.
| Author | : Samuli Schielke |
| Publisher | : Berghahn Books |
| Total Pages | : 174 |
| Release | : 2012-06-01 |
| Genre | : Social Science |
| ISBN | : 0857455079 |
Everyday practice of religion is complex in its nature, ambivalent and at times contradictory. The task of an anthropology of religious practice is therefore precisely to see how people navigate and make sense of that complexity, and what the significance of religious beliefs and practices in a given setting can be. Rather than putting everyday practice and normative doctrine on different analytical planes, the authors argue that the articulation of religious doctrine is also an everyday practice and must be understood as such.
| Author | : Simon R. Blackburn |
| Publisher | : Cambridge University Press |
| Total Pages | : 294 |
| Release | : 2007-10-18 |
| Genre | : Mathematics |
| ISBN | : 9780521882170 |
How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory.
| Author | : M. Makkai |
| Publisher | : Springer |
| Total Pages | : 317 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540371001 |
| Author | : Ralf Hinze |
| Publisher | : Cambridge University Press |
| Total Pages | : 197 |
| Release | : 2023-07-31 |
| Genre | : Computers |
| ISBN | : 1009317865 |
The first introductory account of using string diagrams to reason in elementary category theory.
| Author | : Jean-Pierre Marquis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 316 |
| Release | : 2008-11-20 |
| Genre | : Science |
| ISBN | : 1402093845 |
From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane’s work in the early 1940’s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics. From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.
| Author | : Dieter Probst |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 392 |
| Release | : 2016-07-25 |
| Genre | : Philosophy |
| ISBN | : 1501502646 |
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.
