Galois Theories

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.


"This is a clearly written and readable book covering a lot of interesting and important material, and effectively leading the reader through increasing levels of generality and abstraction." Mathematical Review

Review of the hardback: '… highly recommended or anyone wishing to learn the mathematical side of category theory (rather than its computer-science aspect) … I enjoyed reading it very much.' Proceedings of the Edinburgh Mathematical Society

Review of the hardback: 'A comprehensive account, which may well deepen one's understanding of the classical case.' Mathematika