Read and Download eBook Full
Author: Saunders Mac Lane
Publisher:
Published: 1992
Total Pages: 627
ISBN-13: 9783540977100
DOWNLOAD EBOOKAn introduction to the theory of toposes which begins with illustrative examples and goes on to explain 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.
Author: Saunders MacLane
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 643
ISBN-13: 1461209277
DOWNLOAD EBOOKSheaves 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.
Author: Saunders MacLane
Publisher: Springer Science & Business Media
Published: 1994-10-27
Total Pages: 650
ISBN-13: 0387977104
DOWNLOAD EBOOKSheaves 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.
Author: P.T. Johnstone
Publisher: Courier Corporation
Published: 2014-01-15
Total Pages: 401
ISBN-13: 0486493369
DOWNLOAD EBOOKFocusing 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.
Author: M. P. Fourman
Publisher: Springer
Published: 2006-11-15
Total Pages: 798
ISBN-13: 3540348492
DOWNLOAD EBOOKAuthor: Anastasios Mallios
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 457
ISBN-13: 9401150060
DOWNLOAD EBOOKThis two-volume monograph obtains fundamental notions and results of the standard differential geometry of smooth (CINFINITY) manifolds, without using differential calculus. Here, the sheaf-theoretic character is emphasised. 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 (generalised 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'. Audience: This work is intended for postgraduate students and researchers whose work involves differential geometry, global analysis, analysis on manifolds, algebraic topology, sheaf theory, cohomology, functional analysis or abstract harmonic analysis.
Author: Birger Iversen
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 476
ISBN-13: 3642827837
DOWNLOAD EBOOKThis text exposes the basic features of cohomology of sheaves and its applications. The general theory of sheaves is very limited and no essential result is obtainable without turn ing to particular classes of topological spaces. The most satis factory general class is that of locally compact spaces and it is the study of such spaces which occupies the central part of this text. The fundamental concepts in the study of locally compact spaces is cohomology with compact support and a particular class of sheaves,the so-called soft sheaves. This class plays a double role as the basic vehicle for the internal theory and is the key to applications in analysis. The basic example of a soft sheaf is the sheaf of smooth functions on ~n or more generally on any smooth manifold. A rather large effort has been made to demon strate the relevance of sheaf theory in even the most elementary analysis. This process has been reversed in order to base the fundamental calculations in sheaf theory on elementary analysis.
Author: John L. Bell
Publisher: Courier Corporation
Published: 2008-01-01
Total Pages: 290
ISBN-13: 0486462862
DOWNLOAD EBOOKThis 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.
Author: J. Lambek
Publisher: Cambridge University Press
Published: 1988-03-25
Total Pages: 308
ISBN-13: 9780521356534
DOWNLOAD EBOOKPart I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Author: Masaki Kashiwara
Publisher: Springer Science & Business Media
Published: 2005-12-19
Total Pages: 496
ISBN-13: 3540279504
DOWNLOAD EBOOKCategories 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.
