Topos Theory
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Topos Theory
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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.
Higher Topos Theory
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Author : Jacob Lurie
language : en
Publisher: Princeton University Press
Release Date : 2009-07-26
Higher Topos Theory written by Jacob Lurie and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-26 with Mathematics categories.
In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Toposes And Local Set Theories
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Author : John L. Bell
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
Toposes And Local Set Theories written by John L. Bell and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
Sheaves In Geometry And Logic
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Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sheaves In Geometry And Logic written by Saunders MacLane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Theories Sites Toposes
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Author : Olivia Caramello
language : en
Publisher: Oxford University Press
Release Date : 2018
Theories Sites Toposes written by Olivia Caramello 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 2018 with Mathematics categories.
This book introduces a set of methods and techniques for studying mathematical theories and relating them to each other through the use of Grothendieck toposes.
Topos Theory Why
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Author : Felipe Gago Couso
language : en
Publisher:
Release Date : 1986
Topos Theory Why written by Felipe Gago Couso and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Toposes categories.
A First Course In Topos Quantum Theory
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Author : Cecilia Flori
language : en
Publisher: Springer
Release Date : 2013-03-27
A First Course In Topos Quantum Theory written by Cecilia Flori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-27 with Science categories.
In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.
Forcing And Classifying Topoi
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Author : Andrej Ščedrov
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Forcing And Classifying Topoi written by Andrej Ščedrov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Categories categories.
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.
Categories For The Working Mathematician
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Author : Saunders Mac Lane
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Categories For The Working Mathematician written by Saunders Mac Lane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
Model Theory And Topoi
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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