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Informationen zum Autor Daniel Rosiak Klappentext "This book presents copious and sometimes unexpected examples of sheaf theory, a mathematical tool with promising applications in data science and engineering and in efforts to apply category theory more widely"-- Zusammenfassung 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. Inhaltsverzeichnis Acknowledgments ix Introduction 1 1 Categories 21 2 Prelude to Sheaves: Presheaves 45 3 Universal Constructions 89 4 Topology: A First Pass at Space 109 5 First Look at Sheaves 147 6 There's a Yoneda Lemma for That 171 7 Adjunctions 195 8 Sheaves Revisited 241 9 Cellular Sheaf Cohomology through Examples 277 10 Sheaves on a Site 311 11 Elementary Toposes 369 A Appendix (Revisiting Topology) 411 References 431 Index 439...
