{"product_id":"sheaf-theory-through-examples-isbn-9780262542159","title":"Sheaf Theory through Examples","description":"\u003cb\u003eAn approachable introduction to elementary sheaf theory and its applications beyond pure math.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eSheaves 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, \u003ci\u003eSheaf Theory through Examples\u003c\/i\u003e 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.\u003cbr\u003e \u003cbr\u003eWith an emphasis on developing the theory via a wealth of well-motivated and vividly illustrated examples, \u003ci\u003eSheaf Theory through Examples\u003c\/i\u003e 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.\u003cbr\u003e \u003cbr\u003e\u003ci\u003eSheaf Theory through Examples\u003c\/i\u003e 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.Acknowledgments ix\u003cbr\u003eIntroduction 1\u003cbr\u003e1 Categories 21\u003cbr\u003e2 Prelude to Sheaves: Presheaves 45\u003cbr\u003e3 Universal Constructions 89\u003cbr\u003e4 Topology: A First Pass at Space 109\u003cbr\u003e5 First Look at Sheaves 147\u003cbr\u003e6 There's a Yoneda Lemma for That 171\u003cbr\u003e7 Adjunctions 195\u003cbr\u003e8 Sheaves Revisited 241\u003cbr\u003e9 Cellular Sheaf Cohomology through Examples 277\u003cbr\u003e10 Sheaves on a Site 311\u003cbr\u003e11 Elementary Toposes 369\u003cbr\u003eA Appendix (Revisiting Topology) 411\u003cbr\u003eReferences 431\u003cbr\u003eIndex 439\"Remarkably approachable for those wanting to learn about the theory of sheaves but who do not have an extensive familiarity with the deep abstraction common to mathematical theories in general.\"\u003cbr\u003e\u003cb\u003e—M. Clay, University of Arkansas\u003c\/b\u003e“Rosiak stimulates a shift in perspective—one that will encourage readers from diverse backgrounds to learn sheaf theory and imagine new applications to science, engineering and philosophy.”\u003cbr\u003e—\u003cb\u003eJustin Curry, Professor of Mathematics and Statistics at SUNY Albany\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e \u003c\/b\u003e\u003cbr\u003e“Rosiak's visual imagination and his very detailed treatment of a wide array of examples allow the reader to uncover, as Novalis' \u003ci\u003eNovices of Sais\u003c\/i\u003e, the secrets of sheaf theory, perhaps the deepest mathematical construction of the twentieth century.”\u003cbr\u003e\u003cb\u003e—Fernando Zalamea, Professor of Mathematics, Universidad Nacional de Colombia\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e \u003c\/b\u003e\u003cbr\u003e“With precise definitions and brimming with creative and illustrative examples, ranging from the Penrose Triangle to image processing, \u003ci\u003eSheaf Theory through Examples\u003c\/i\u003e is probably the most pleasant way to learn about sheaves.”\u003cbr\u003e\u003cb\u003e—David Spivak, Chief Scientist, Topos Institute\u003c\/b\u003eDaniel Rosiak is a Research Associate at the Inamori International Center for Ethics and Excellence at Case Western Reserve University.","brand":"The MIT Press","offers":[{"title":"Default Title","offer_id":46304551862501,"sku":"NP9780262542159","price":65.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780262542159.jpg?v=1767736508","url":"https:\/\/k12savings.com\/products\/sheaf-theory-through-examples-isbn-9780262542159","provider":"K12savings","version":"1.0","type":"link"}