Sketches of an Elephant: A Topos Theory Compendium

Author: P. T. Johnstone

Publisher: Oxford University Press

ISBN: 9780198515982

Category: Mathematics

Page: 716

View: 6208

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.

Category Theory in Context

Author: Emily Riehl

Publisher: Courier Dover Publications

ISBN: 0486820807

Category: Mathematics

Page: 272

View: 566

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.

From Sets and Types to Topology and Analysis

Towards Practicable Foundations for Constructive Mathematics

Author: Laura Crosilla,Peter Schuster

Publisher: Oxford University Press on Demand

ISBN: 0198566514

Category: Mathematics

Page: 350

View: 4707

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.

From a Geometrical Point of View

A Study of the History and Philosophy of Category Theory

Author: Jean-Pierre Marquis

Publisher: Springer Science & Business Media

ISBN: 1402093845

Category: Science

Page: 310

View: 932

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.

Reality and Measurement in Algebraic Quantum Theory

NWW 2015, Nagoya, Japan, March 9-13

Author: Masanao Ozawa,Jeremy Butterfield,Hans Halvorson,Miklós Rédei,Yuichiro Kitajima,Francesco Buscemi

Publisher: Springer

ISBN: 9811324875

Category: Mathematics

Page: 396

View: 2826

This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.

Kategorien und Funktoren

Author: Bodo Pareigis

Publisher: N.A


Category: Categories (Mathematics)

Page: 192

View: 9613


Ideen Zu Einer Geographie Der Pflanzen

Author: Alexander Homboldt

Publisher: BoD – Books on Demand

ISBN: 3955075036


Page: 200

View: 9154

Diese Veroffentlichung von Alexander von Humboldt ist die Synopse der bis dahin (1805) durchgefuhrten Forschungsreisen. Er versuchte sich hier erstmals an einer Systematik der weltweiten Geographie der Pflanzen und schuf damit ein revolutioares und weithin beachtetes Werk.


Die großen Fragen der Philosophie

Author: Simon Blackburn

Publisher: N.A

ISBN: 9783863120511


Page: 260

View: 5107



Author: Edward W. Said

Publisher: N.A

ISBN: 9783100710086

Category: Europa - Orientbild - Kultur - Geschichte 1800-2000

Page: 459

View: 8126


Regular Solids and Isolated Singularities

Author: Klaus Lamotke

Publisher: Vieweg+Teubner Verlag

ISBN: 9783528089580

Category: Mathematics

Page: 224

View: 4201

The last book XIII of Euclid's Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl~fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the finite rotation groups. He introduced complex coordinates and by means of invariant theory associated polynomial equations with these groups. These equations in turn describe isolated singularities of complex surfaces. The structure of the singularities is investigated by methods of commutative algebra, algebraic and complex analytic geometry, differential and algebraic topology. A paper by DuVal from 1934 (see the References), in which resolutions play an important rele, marked an early stage of these investigations. Around 1970 Klein's polynomials were again related to new mathematical ideas: V. I. Arnold established a hierarchy of critical points of functions in several variables according to growing com plexity. In this hierarchy Kleinls polynomials describe the "simple" critical points.

Welten im Zusammenstoss

Author: Immanuel Velikovsky

Publisher: Julia White Publishing

ISBN: 3934402917


Page: 462

View: 5540


Der Antimachiavell

Author: Friedrich der Grosse

Publisher: CreateSpace

ISBN: 9781469998329


Page: 44

View: 9783

Friedrich II., auch Friedrich der Große oder der Alte Fritz genannt (* 24. Januar 1712 in Berlin ; + 17. August 1786 in Potsdam), war ab 1740 König in und ab 1772 König von Preußen sowie Kurfürst von Brandenburg. Die von ihm gegen Österreich geführten drei Schlesischen Kriege um den Besitz Schlesiens führten zum Deutschen Dualismus. Nach dem letzten dieser Kriege, dem Siebenjährigen von 1756 bis 1763, war Preußen als fünfte Großmacht in der europäischen Pentarchie anerkannt neben Frankreich, Großbritannien, Österreich und Russland. Friedrich gilt als ein Repräsentant des aufgeklärten Absolutismus. So bezeichnete er sich selbst als Ersten Diener des Staates".Anti-Machiavel heißt ein Werk, das sich aus dem Briefwechsel zwischen Friedrich des II. von Preußen und Voltaire 1736-1740 heraus entwickelt hatte. Der damalige Erbprinz hatte im Alter von 24 Jahren mit dem Philosophen und Schriftsteller durch einen Brief vom 8. August 1736 Kontakt aufgenommen.