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  "body": "\n## Summary\n\nA Galois category is a [[category|A2DE66937D]] with a [[functor|28NQ0KRHD3]] to finite sets, called a fibre functor.\nThe pair satisfies axioms modelled on finite covering spaces and on finite separable field extensions.\nThe main theorem says that such a category is equivalent to the category of finite sets with a continuous action of a [[profinite group|KA0YDB6QXE]].\nThis group is the automorphism group of the fibre functor.\nIt is the abstract frame of [[Grothendieck's Galois theory|CX7BDQ47ZK]].\nWith finite étale covers of a connected scheme it defines the [[étale fundamental group|KJ11DAXMR0]].\n\n## Explanations\n\n### L1 human\n\nClassical Galois theory and the theory of covering spaces share one pattern: a group acts on a fibre, and the objects correspond to sets with an action of that group.\nA Galois category isolates the properties needed for this pattern.\nIts objects behave like finite covers, and the fibre functor sends each one to the finite set of points above a base point.\nFor example, finite sets with an action of a finite group $G$, with the functor that forgets the action, form a Galois category, and the group it recovers is $G$.\n",
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