Topos Theory

Download Topos Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Topos Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Topos Theory

DOWNLOAD
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.

Toposes And Local Set Theories

DOWNLOAD
Author : J. L. Bell
language : en
Publisher: Dover Publications
Release Date : 2013-12-11

Toposes And Local Set Theories written by J. L. Bell and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with categories.

This introduction to topos theory examines local set theories, fundamental properties of toposes, sheaves, locale-valued sets, and natural and real numbers in local set theories. 1988 edition.

A First Course In Topos Quantum Theory

DOWNLOAD
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.

Topos Theory

DOWNLOAD
Author : P.T. Johnstone
language : en
Publisher: Courier Corporation
Release Date : 2014-01-05

Theories Sites Toposes

DOWNLOAD
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.

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.

Temporal Type Theory

DOWNLOAD
Author : Patrick Schultz
language : en
Publisher: Springer
Release Date : 2019-01-29

Temporal Type Theory written by Patrick Schultz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-29 with Mathematics categories.

This innovative monograph explores a new mathematical formalism in higher-order temporal logic for proving properties about the behavior of systems. Developed by the authors, the goal of this novel approach is to explain what occurs when multiple, distinct system components interact by using a category-theoretic description of behavior types based on sheaves. The authors demonstrate how to analyze the behaviors of elements in continuous and discrete dynamical systems so that each can be translated and compared to one another. Their temporal logic is also flexible enough that it can serve as a framework for other logics that work with similar models. The book begins with a discussion of behavior types, interval domains, and translation invariance, which serves as the groundwork for temporal type theory. From there, the authors lay out the logical preliminaries they need for their temporal modalities and explain the soundness of those logical semantics. These results are then applied to hybrid dynamical systems, differential equations, and labeled transition systems. A case study involving aircraft separation within the National Airspace System is provided to illustrate temporal type theory in action. Researchers in computer science, logic, and mathematics interested in topos-theoretic and category-theory-friendly approaches to system behavior will find this monograph to be an important resource. It can also serve as a supplemental text for a specialized graduate topics course.

Basic Category Theory

DOWNLOAD
Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24

Basic Category Theory written by Tom Leinster and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.

A short introduction ideal for students learning category theory for the first time.

Higher Topos Theory

DOWNLOAD
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.

Sketches Of An Elephant

DOWNLOAD
Author : Peter T. Johnstone
language : en
Publisher: Oxford University Press
Release Date : 2002

Sketches Of An Elephant written by Peter T. Johnstone 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 2002 with Toposes categories.

Category Theory For The Sciences

DOWNLOAD
Author : David I. Spivak
language : en
Publisher: MIT Press
Release Date : 2014-10-10

Category Theory For The Sciences written by David I. Spivak and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-10 with Mathematics categories.

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

Topos Theory

Recent Posts