Category Theory pp 157-173 | Cite as
Precategories and Galois theory
Part I
First Online:
Abstract
We give a new version of Galois theory in categories in which normal extensions are replaced by arbitrary extensions for which the “pullback functor” is monadic, and their Galois groupoids are replaced by internal pregroupoids; we obtain the “fundamental theorem of Galois theory” using just simple remarks on internal precategories and change of universe for internal functors.
Keywords
Commutative Ring Galois Group Fundamental Theorem Central Extension Full Subcategory
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References
- [1]M. Bunge, Open covers and the fundamental localic groupoid of a topos, McGill Univ. Math. Preprint 89–33 (1989).Google Scholar
- [2]A. Grothendieck, Revêtements étales et groupe fondamental, SGA 1, Springer Lecture Notes in Math. 269 (1972).Google Scholar
- [3]G. Janelidze, Galois extensions of commutative rings by profinite families of groups, Transactions of Razmadze Math. Inst. of the Georgian Acad. Sci. 74 (1983), 39–51 (in Russian).MathSciNetGoogle Scholar
- [4]G. Janelidze, Magid theorem in categories, Bull. Georgian Acad. Sci. 114(3) (1984), 497–500 (in Russian).MathSciNetGoogle Scholar
- [5]G. Janelidze, A generalization of the theory of covering spaces, IV International Conf. in Topology and its Applications, Abstract of Reports, Dubrovnic (1985).Google Scholar
- [6]G. Janelidze, (G.Z. Dzhanelidze), The fundamental theorem of Galois theory, Math. USSR Sbornik 64(2) (1989), 359–374.MathSciNetCrossRefzbMATHGoogle Scholar
- [7]G. Janelidze, Pure Galois theory in categories, U.C.N.W. Pure Math. Preprint 87.20 (Bangor 1987) (and to appear in Journal of Algebra).Google Scholar
- [8]G. Janelidze, Galois theory in categories: the new example of differential fields, Categorical Topology (Proc. Conf. in Prague), World Scientific (1988), 369–380.Google Scholar
- [9]G. Janelidze, What is a double central extension — the question was given by Ronnie Brown, to appear.Google Scholar
- [10]G. Janelidze, A note on Barr-Diaconescu covering theory, to appear.Google Scholar
- [11]G. Janelidze, Change of universe in the category of internal functors, McGill Univ. Math. Preprint 90–11 (1990).Google Scholar
- [12]J. Kennison, What is the fundamental group?, J. Pure Appl. Algebra 59 (1989), 187–200.MathSciNetCrossRefzbMATHGoogle Scholar
- [13]A.R. Magid, The separable Galois theory of commutative rings, Marsel Dekker (1974).Google Scholar
- [14]R.S. Pierce, Modules over commutative regular rings, Mem. AMS 70 (1967).Google Scholar
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© Springer-Verlag 1991