Elements Of Sheaf Theory
DOWNLOAD
Download Elements Of Sheaf Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Elements Of Sheaf 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
Elements Of Sheaf Theory
DOWNLOAD
Author : Daniel Bert Abrams
language : en
Publisher:
Release Date : 1987
Elements Of Sheaf Theory written by Daniel Bert Abrams and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Homology theory categories.
Handbook Of Categorical Algebra Volume 3 Sheaf Theory
DOWNLOAD
Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 1994-12-08
Handbook Of Categorical Algebra Volume 3 Sheaf Theory written by Francis Borceux 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 1994-12-08 with Mathematics categories.
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.
Sheaf Theory Through Examples
DOWNLOAD
Author : Daniel Rosiak
language : en
Publisher: MIT Press
Release Date : 2022-10-25
Sheaf Theory Through Examples written by Daniel Rosiak and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-25 with Mathematics categories.
An approachable introduction to elementary sheaf theory and its applications beyond pure math. Sheaves are mathematical constructions concerned with passages from local properties to global ones. They have played a fundamental role in the development of many areas of modern mathematics, yet the broad conceptual power of sheaf theory and its wide applicability to areas beyond pure math have only recently begun to be appreciated. Taking an applied category theory perspective, Sheaf Theory through Examples provides an approachable introduction to elementary sheaf theory and examines applications including n-colorings of graphs, satellite data, chess problems, Bayesian networks, self-similar groups, musical performance, complexes, and much more. With an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, Sheaf Theory through Examples supplements the formal development of concepts with philosophical reflections on topology, category theory, and sheaf theory, alongside a selection of advanced topics and examples that illustrate ideas like cellular sheaf cohomology, toposes, and geometric morphisms. Sheaf Theory through Examples seeks to bridge the powerful results of sheaf theory as used by mathematicians and real-world applications, while also supplementing the technical matters with a unique philosophical perspective attuned to the broader development of ideas.
Sheaf Theory
DOWNLOAD
Author : Glen E. Bredon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sheaf Theory written by Glen E. Bredon 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 2012-12-06 with Mathematics categories.
This book is primarily concerned with the study of cohomology theories of general topological spaces with "general coefficient systems." Sheaves play several roles in this study. For example, they provide a suitable notion of "general coefficient systems." Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas important to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the concept of the "tautness" of a subspace (an adaptation of an analogous notion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The factthat sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a "single space" theory.
Geometry Of Vector Sheaves
DOWNLOAD
Author : Anastasios Mallios
language : en
Publisher: Springer Science & Business Media
Release Date : 1998
Geometry Of Vector Sheaves written by Anastasios Mallios 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 1998 with Mathematics categories.
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.
Sheaves In Geometry And Logic
DOWNLOAD
Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sheaves In Geometry And Logic written by Saunders MacLane 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 2012-12-06 with Mathematics categories.
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.
Conceptual Categories And The Structure Of Reality Theoretical And Empirical Approaches
DOWNLOAD
Author : Paul M.W. Hackett
language : en
Publisher: Frontiers Media SA
Release Date : 2019-01-21
Conceptual Categories And The Structure Of Reality Theoretical And Empirical Approaches written by Paul M.W. Hackett and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with categories.
In this eBook, Conceptual Categories and the Structure of Reality, the title very well describes the book's content. Within the book's pages a selection of academics from a variety of human behaviour, human/social science and humanities disciplines write about their research all of which can be typified by their consideration of how categories are used to structure understanding of phenomena. These authors have considered how reality may be understood through notions such as categorial and structural ontologies, part-whole relatoinships (mereology), the qualitative, quantitative and philosophical use of the facet theory approach to research, mapping sentences and declarative mapping sentence, hermeneutics, concepts and constructs, similarities and differences. The resulting collection presents the foregoing conceptual and empirical approaches to knowledge development in general (chapter 1&3 Hackett); Phillips and Wislons' review of compositional syntax in bird calls (chapter 2); neurobehavioral decision systems (chapter 4 Foxall); representations of human psychological processes (chapter 5 Juan-Miguel López-Gil; Rosa Gil; Roberto García); free associations mirroring and its relation to self- and world-related concepts (chapter 6 Martin Kuška; Radek Trnka; Aleš Antonín Kuběna; Jiří Růžička); local knowledge and going beyond the data (chapter 7 Steven Phillips); categorical etiologies of speech sound disorders (chapter 8 Kelly Farquharson); similarity of visual appearance (chapter 9 Nao Nakatsuji; Hisayasu Ihara; Takeharu Seno; Hiroshi Ito); and a consideration of the seminal writing of David Oderberg's on the categorial classification of reality (chapter 10 Hackett).
Differential Sheaves And Connections A Natural Approach To Physical Geometry
DOWNLOAD
Author : Anastasios Mallios
language : en
Publisher: World Scientific
Release Date : 2015-09-17
Differential Sheaves And Connections A Natural Approach To Physical Geometry written by Anastasios Mallios and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-17 with Mathematics categories.
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
An Introduction To Alysidal Algebra V Phenomenological Components
DOWNLOAD
Author : Antonio Nescolarde-Selva Josué
language : en
Publisher: Infinite Study
Release Date :
An Introduction To Alysidal Algebra V Phenomenological Components written by Antonio Nescolarde-Selva Josué and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This paper aims to refer to a subjective approach to a type of complex system: human ecosystems, referred to as deontical impure systems (DIS) to capture a set of properties fundamental to the distinction between human and natural ecosystems. There are four main phenomenological components: directionality, intensity, connection energy and volume. The paper establishes thermodynamics of deontical systems based on the Law of Zipf and the temperature of information.
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture
DOWNLOAD
Author : Joel Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture written by Joel Friedman 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 2014-12-20 with Mathematics categories.
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.