Applications of Sheaves

Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra and Analysis, Durham, July 9-21, 1977

Author: M. P. Fourman,C. J. Mulvey,D. S. Scott

Publisher: Springer

ISBN: 3540348492

Category: Mathematics

Page: 779

View: 884

Posted in Mathematics

Categories and Sheaves

Author: Masaki Kashiwara,Pierre Schapira

Publisher: Springer Science & Business Media

ISBN: 3540279490

Category: Mathematics

Page: 498

View: 8749

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.
Posted in Mathematics

Categorical Algebra and its Applications

Proceedings of a Conference, Held in Louvain-la-Neuve, Belgium, July 26 - August 1, 1987

Author: Francis Borceux

Publisher: Springer

ISBN: 3540459855

Category: Mathematics

Page: 382

View: 6085

Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.
Posted in Mathematics

Equivariant Sheaves and Functors

Author: Joseph Bernstein,Valery Lunts

Publisher: Springer

ISBN: 3540484302

Category: Mathematics

Page: 146

View: 9519

The equivariant derived category of sheaves is introduced. All usual functors on sheaves are extended to the equivariant situation. Some applications to the equivariant intersection cohomology are given. The theory may be useful to specialists in representation theory, algebraic geometry or topology.
Posted in Mathematics

Definable Additive Categories

Purity and Model Theory

Author: Mike Prest

Publisher: American Mathematical Soc.

ISBN: 0821847678

Category: Mathematics

Page: 109

View: 5801

Most of the model theory of modules works, with only minor modifications, in much more general additive contexts (such as functor categories, categories of comodules, categories of sheaves). Furthermore, even within a given category of modules, many subcategories form a ``self-sufficient'' context in which the model theory may be developed without reference to the larger category of modules. The notion of a definable additive category covers all these contexts. The (imaginaries) language which one uses for model theory in a definable additive category can be obtained from the category (of structures and homomorphisms) itself, namely, as the category of those functors to the category of abelian groups which commute with products and direct limits. Dually, the objects of the definable category--the modules (or functors, or comodules, or sheaves)--to which that model theory applies may be recovered as the exact functors from the, small abelian, category (the category of pp-imaginaries) which underlies that language.
Posted in Mathematics

Proceedings

Author: N.A

Publisher: N.A

ISBN: 9780780350649

Category: Computers

Page: 538

View: 7525

Posted in Computers

Handbook of Categorical Algebra: Volume 3, Sheaf Theory

Author: Francis Borceux

Publisher: Cambridge University Press

ISBN: 9780521441803

Category: Mathematics

Page: 522

View: 9479

The Handbook of Categorical Algebra is intended to give, in three volumes, a rather detailed account of what, ideally, everybody working in category theory should know, whatever the specific topic of research they have chosen. The book is planned also to serve as a reference book for both specialists in the field and all those using category theory as a tool. Volume 3 begins with the essential aspects of the theory of locales, proceeding to a study in chapter 2 of the sheaves on a locale and on a topological space, in their various equivalent presentations: functors, etale maps or W-sets. Next, this situation is generalized to the case of sheaves on a site and the corresponding notion of Grothendieck topos is introduced. Chapter 4 relates the theory of Grothendieck toposes with that of accessible categories and sketches, by proving the existence of a classifying topos for all coherent theories.
Posted in Mathematics

Methods of Homological Algebra

Author: Sergei I. Gelfand,Yuri I. Manin

Publisher: Springer Science & Business Media

ISBN: 3662124920

Category: Mathematics

Page: 372

View: 6961

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.
Posted in Mathematics

Motives

Author: Uwe Jannsen,Steven L. Kleiman,Jean Pierre Serre

Publisher: Amer Mathematical Society

ISBN: 9780821816356

Category: Mathematics

Page: 1423

View: 5422

Posted in Mathematics

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5064

Posted in Mathematics

Collected Works: Michael Atiyah Collected Works

Volume 1: Early Papers; General Papers

Author: Michael Atiyah

Publisher: N.A

ISBN: 9780198532750

Category: Mathematics

Page: 392

View: 5888

One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.
Posted in Mathematics

Homological Algebra

Author: S.I. Gelfand,Yu.I. Manin

Publisher: Springer Science & Business Media

ISBN: 9783540533733

Category: Mathematics

Page: 222

View: 1316

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.
Posted in Mathematics

Categorical Foundations

Special Topics in Order, Topology, Algebra, and Sheaf Theory

Author: Maria Cristina Pedicchio,Walter Tholen,G. C. Rota

Publisher: Cambridge University Press

ISBN: 9780521834148

Category: Mathematics

Page: 417

View: 6730

The book offers categorical introductions to order, topology, algebra and sheaf theory, suitable for graduate students, teachers and researchers of pure mathematics.
Posted in Mathematics

The Heart of Cohomology

Author: Goro Kato

Publisher: Springer Science & Business Media

ISBN: 1402050364

Category: Mathematics

Page: 191

View: 8860

If you have not heard about cohomology, The Heart of Cohomology may be suited for you. The book gives Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology. In addition, the book examines cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family.
Posted in Mathematics

Categories and Modules with K-Theory in View

Author: A. J. Berrick,M. E. Keating

Publisher: Cambridge University Press

ISBN: 9780521632768

Category: Mathematics

Page: 361

View: 7664

This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.
Posted in Mathematics

Topos Theory

Author: P.T. Johnstone

Publisher: Courier Corporation

ISBN: 0486493369

Category: Mathematics

Page: 400

View: 6352

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.
Posted in Mathematics

D-Modules, Perverse Sheaves, and Representation Theory

Author: Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki

Publisher: Springer Science & Business Media

ISBN: 0817645233

Category: Mathematics

Page: 412

View: 8462

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.
Posted in Mathematics

Geometry of Vector Sheaves

An Axiomatic Approach to Differential Geometry

Author: Anastasios Mallios

Publisher: Springer Science & Business Media

ISBN: 9780792350040

Category: Geometry, Differential

Page: 441

View: 4313

This text is part of a two-volume monograph which obtains fundamental notions and results of the standard differential geometry of smooth manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasized. This has theoretical advantages such as greater perspective, clarity and unification, but also practical benefits ranging from elementary particle physics, via gauge theories and theoretical cosmology (differential spaces), to non-linear PDEs (generalized functions). Thus, more general applications, which are no longer smooth in the classical sense, can be coped with. The treatise might also be construed as a new systematic endeavour to confront the ever-increasing notion that the world around us is far from being smooth enough.
Posted in Geometry, Differential