Sheaves In Geometry And Logic PDF Download
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Author | : Saunders Mac Lane |
Publisher | : |
Total Pages | : 627 |
Release | : 1992 |
Genre | : Algebraische Geometrie - Garbentheorie |
ISBN | : 9783540977100 |
Download Sheaves in Geometry and Logic Book in PDF, ePub and Kindle
An 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 |
Total Pages | : 643 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461209277 |
Download Sheaves in Geometry and Logic Book in PDF, ePub and Kindle
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.
Author | : Saunders MacLane |
Publisher | : Springer Science & Business Media |
Total Pages | : 650 |
Release | : 1994-10-27 |
Genre | : Mathematics |
ISBN | : 0387977104 |
Download Sheaves in Geometry and Logic Book in PDF, ePub and Kindle
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.
Author | : P.T. Johnstone |
Publisher | : Courier Corporation |
Total Pages | : 401 |
Release | : 2014-01-15 |
Genre | : Mathematics |
ISBN | : 0486493369 |
Download Topos Theory Book in PDF, ePub and Kindle
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.
Author | : M. P. Fourman |
Publisher | : Springer |
Total Pages | : 798 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540348492 |
Download Applications of Sheaves Book in PDF, ePub and Kindle
Author | : J. Lambek |
Publisher | : Cambridge University Press |
Total Pages | : 308 |
Release | : 1988-03-25 |
Genre | : Mathematics |
ISBN | : 9780521356534 |
Download Introduction to Higher-Order Categorical Logic Book in PDF, ePub and Kindle
Part 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 | : Anastasios Mallios |
Publisher | : Springer Science & Business Media |
Total Pages | : 457 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401150060 |
Download Geometry of Vector Sheaves Book in PDF, ePub and Kindle
This 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 | : Masaki Kashiwara |
Publisher | : Springer Science & Business Media |
Total Pages | : 496 |
Release | : 2005-12-19 |
Genre | : Mathematics |
ISBN | : 3540279504 |
Download Categories and Sheaves Book in PDF, ePub and Kindle
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.
Author | : Ernest E. Shult |
Publisher | : Springer Science & Business Media |
Total Pages | : 682 |
Release | : 2010-12-13 |
Genre | : Mathematics |
ISBN | : 3642156274 |
Download Points and Lines Book in PDF, ePub and Kindle
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups. These tools could be useful in shortening the enormously lengthy classification of finite simple groups. Similarly, recognizing ruled manifolds by axioms on light trajectories offers a way for a physicist to recognize the action of a Lie group in a context where it is not clear what Hamiltonians or Casimir operators are involved. The presentation is self-contained in the sense that proofs proceed step-by-step from elementary first principals without further appeal to outside results. Several chapters have new heretofore unpublished research results. On the other hand, certain groups of chapters would make good graduate courses. All but one chapter provide exercises for either use in such a course, or to elicit new research directions.
Author | : Saunders Mac Lane |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475747217 |
Download Categories for the Working Mathematician Book in PDF, ePub and Kindle
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.