Categories And Sheaves

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Categories And Sheaves

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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-10-20

Categories And Sheaves written by Masaki Kashiwara 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 2005-10-20 with Mathematics categories.

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Exact Categories And Categories Of Sheaves

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Author : M. Barr
language : en
Publisher: Springer
Release Date : 2006-11-15

Exact Categories And Categories Of Sheaves written by M. Barr 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.

Sheaves On Manifolds

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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-01

Sheaves On Manifolds written by Masaki Kashiwara 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 2002-05-01 with Mathematics categories.

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

Category Theory For The Sciences

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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.

Sheaves In Topology

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Author : Alexandru Dimca
language : en
Publisher:
Release Date : 2011-03-30

Sheaves In Topology written by Alexandru Dimca and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-30 with categories.

Manifolds Sheaves And Cohomology

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Author : Torsten Wedhorn
language : en
Publisher: Springer
Release Date : 2016-07-25

Manifolds Sheaves And Cohomology written by Torsten Wedhorn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Mathematics categories.

This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.

Topology Of Singular Spaces And Constructible Sheaves

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Author : Jörg Schürmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-24

Topology Of Singular Spaces And Constructible Sheaves written by Jörg Schürmann 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 2003-10-24 with Mathematics categories.

Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.

Algebra Chapter 0

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Author : Paolo Aluffi
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

Algebra Chapter 0 written by Paolo Aluffi 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 2009 with Mathematics categories.

Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Algebra Arithmetic And Geometry

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Author : Yuri Tschinkel
language : vi
Publisher: Springer Science & Business Media
Release Date : 2010-08-05

Algebra Arithmetic And Geometry written by Yuri Tschinkel 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 2010-08-05 with Mathematics categories.

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

D Modules Perverse Sheaves And Representation Theory

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Author : Kiyoshi Takeuchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-12

D Modules Perverse Sheaves And Representation Theory written by Kiyoshi Takeuchi 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 2007-10-12 with Mathematics categories.

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.