Abstract
These notes describe the formalism of Galois categories and fundamental groups, as introduced by A. Grothendieck in [SGA1, Chap. V]. This formalism stems from Galois theory for topological covers and can be regarded as the natural categorical generalization of it. But, far beyond providing a uniform setting for the preexisting Galois theories as those of topological covers and field extensions, this formalism gave rise to the construction and theory of the étale fundamental group of schemes −one of the major achievements of modern algebraic geometry.
Mathematics Subject Classification (2010). 14-01, 18-01.
Proceedings of the G.A.M.S.C. summer school (Istanbul, June 9th–June 20th, 2008).
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Cadoret, A. (2013). Galois Categories. In: Dèbes, P., Emsalem, M., Romagny, M., Uludağ, A. (eds) Arithmetic and Geometry Around Galois Theory. Progress in Mathematics, vol 304. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0487-5_3
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DOI: https://doi.org/10.1007/978-3-0348-0487-5_3
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