Sheaf Theory Through Examples

Description

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. f000200_9780262370424 f000300_9780262370424 c000400_9780262370424 c000500_9780262370424 c001100_9780262370424 c001700_9780262370424 c002000_9780262370424 c002500_9780262370424 c002900_9780262370424 c003600_9780262370424 c004100_9780262370424 c004500_9780262370424 c005000_9780262370424 c005500_9780262370424 c006100_9780262370424 r006700_9780262370424 c006800_9780262370424