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Classifying Spaces and Classifying Topoi

Author : Izak Moerdijk

Publisher : Springer

Page : 100 pages

File Size : 18,95 MB

Release : 2006-11-14

Category : Mathematics

ISBN : 3540449124

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Book Description

This monograph presents a new, systematic treatment of the relation between classifying topoi and classifying spaces of topological categories. Using a new generalized geometric realization which applies to topoi, a weak homotopy equival- ence is constructed between the classifying space and the classifying topos of any small (topological) category. Topos theory is then applied to give an answer to the question of what structures are classified by "classifying" spaces. The monograph should be accessible to anyone with basic knowledge of algebraic topology, sheaf theory, and a little topos theory.





Forcing and Classifying Topoi

Author : Andrej Ščedrov

Publisher : American Mathematical Soc.

Page : 106 pages

File Size : 26,42 MB

Release : 1984

Category : Categories

ISBN : 0821822942

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Book Description

We give a general method of forcing over categories as a category-theoretic universal construction which subsumes, on one hand, all known instances of forcing in set theory, Boolean and Heyting valued models and sheaf interpretations for both classical and intuitionistic formal systems; and, on the other hand, constructions of classifying topoi in topos theory.



Sheaves in Geometry and Logic

Author : Saunders MacLane

Publisher : Springer Science & Business Media

Page : 643 pages

File Size : 41,35 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461209277

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Book Description

Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it explains 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.



Sketches of an Elephant: A Topos Theory Compendium

Author : P. T. Johnstone

Publisher : Oxford University Press

Page : 836 pages

File Size : 31,33 MB

Release : 2002-09-12

Category : Computers

ISBN : 9780198515982

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Book Description

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.



Handbook of Philosophical Logic

Author : D.M. Gabbay

Publisher : Springer Science & Business Media

Page : 382 pages

File Size : 24,48 MB

Release : 2005-12-15

Category : Philosophy

ISBN : 1402030924

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Book Description

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications



New Spaces in Mathematics

Author : Mathieu Anel

Publisher : Cambridge University Press

Page : 601 pages

File Size : 38,12 MB

Release : 2021-04

Category : Mathematics

ISBN : 1108490638

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Book Description

In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.



Integrable Systems and Foliations

Author : Claude Albert

Publisher : Springer Science & Business Media

Page : 219 pages

File Size : 42,50 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 1461241340

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Book Description

The articles in this volume are an outgrowth of a colloquium "Systemes Integrables et Feuilletages," which was held in honor of the sixtieth birthday of Pierre Molino. The topics cover the broad range of mathematical areas which were of keen interest to Molino, namely, integral systems and more generally symplectic geometry and Poisson structures, foliations and Lie transverse structures, transitive structures, and classification problems.



Topoi

Author : Robert Goldblatt

Publisher : Courier Corporation

Page : 578 pages

File Size : 28,64 MB

Release : 2013-07-25

Category : Mathematics

ISBN : 048631796X

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Book Description

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.



Issues in Biological, Biochemical, and Evolutionary Sciences Research: 2012 Edition

Author :

Publisher : ScholarlyEditions

Page : 777 pages

File Size : 13,73 MB

Release : 2013-01-10

Category : Science

ISBN : 148164548X

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Book Description

Issues in Biological, Biochemical, and Evolutionary Sciences Research: 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Macromolecular Research. The editors have built Issues in Biological, Biochemical, and Evolutionary Sciences Research: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Macromolecular Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Biological, Biochemical, and Evolutionary Sciences Research: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.