Sheaf Theory Through Examples

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Sheaf Theory Through Examples

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 Through Examples

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

Sheaf Theory written by Glen E. Bredon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Sheaf theory categories.

Elements Of Sheaf Theory

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.

Teichm Ller Theory And Applications To Geometry Topology And Dynamics

Teichm Ller Theory And Applications To Geometry Topology And Dynamics written by John Hamal Hubbard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Sheaf Semantics For Concurrent Interacting Objects

Sheaf Semantics For Concurrent Interacting Objects written by Joseph Goguen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Semantics categories.

Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards

Index To Theses With Abstracts Accepted For Higher Degrees By The Universities Of Great Britain And Ireland And The Council For National Academic Awards written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Dissertations, Academic categories.

Theses on any subject submitted by the academic libraries in the UK and Ireland.

Applications Of Sheaf Theory To Function Algebras

Applications Of Sheaf Theory To Function Algebras written by Albert Emerson Hurd and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Functional analysis categories.

A representation theory is developed for an arbitrary commutative algebra with identity in terms of al algebra of continuous functions on a suitable topological space. A brief survey is presented of the theory of coherent analytic sheaves. No attempt at completeness is made; the object being to collect in one place the definitions and results. The sheaf-theoretic results are then used to investigate algebras of holomorphic functions on the special class of complex manifolds, the Stein manifolds. A simple example is presented to point out the error of a theorem stating that the functions on the maximal ideal space of a Banach algebra, which came from elements of the algebra via the Gelfand respresentation, enjoy a certain local characterization, much as do analytic functions on a complex manifold, or continuous functions on a topological space. The appendix contains a proof of the generalization of the Stone-Weierstrass theorem. (Author).

A General Cohomology Theory Of Sheaves

A General Cohomology Theory Of Sheaves written by Charles Edward Watts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Homology theory categories.

The American Mathematical Monthly

The American Mathematical Monthly written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematicians categories.

Includes articles, as well as notes and other features, about mathematics and the profession.