Pure Galois theory in categories. (English) Zbl 0702.18006
Grothendieck lifted the order-reversing connection, between subgroups of the Galois group G and field extensions, to a contravariant category equivalence between finite G-sets and certain algebras. While there have been several beautiful extensions of this result in the last fifteen years, the present paper seems to be the first “purely” categorical version which gives Grothendieck’s version and some of the generalizations with no further work. The author was influenced by A. R. Magid [The separable Galois theory of commutative rings. New York: Marcel Dekker (1974; Zbl 0284.13004)]. A feature of the approach is that the Galois group is replaced by a groupoid internal to a category and is obtained as the value of a functor at a chaotic groupoid internal to another category.
Reviewer: R.H.Street
MSC:
| 18D35 | Structured objects in a category (MSC2010) |
| 12F10 | Separable extensions, Galois theory |
Citations:
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