Ebook: Galois Theories

Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context. The authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience, the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. For all algebraists and category theorists this book will be a rewarding read.