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1.

図書

図書
Francis Borceux, George Janelidze
出版情報: Cambridge : Cambridge University Press, 2001  xiv, 341 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 72
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目次情報: 続きを見る
Preface
Classical Galois theory / 1:
Algebraic extensions / 1.1:
Separable extensions / 1.2:
Normal extensions / 1.3:
Galois extensions / 1.4:
Galois theory of Grothendieck / 2:
Algebras on a field / 2.1:
Extension of scalars / 2.2:
Split algebras / 2.3:
The Galois equivalence / 2.4:
Infinitary Galois theory / 3:
Finitary Galois subextensions / 3.1:
Infinitary Galois groups / 3.2:
Classical infinitary Galois theory / 3.3:
Profinite topological spaces / 3.4:
Infinitary extension of the Galois theory of Grothendieck / 3.5:
Categorical Galois theory of commutative rings / 4:
Stone duality / 4.1:
Pierce representation of a commutative ring / 4.2:
The adjoint of the 'spectrum' functor / 4.3:
Descent morphisms / 4.4:
Morphisms of Galois descent / 4.5:
Internal presheaves / 4.6:
The Galois theorem for rings / 4.7:
Categorical Galois theorem and factorization systems / 5:
The abstract categorical Galois theorem / 5.1:
Central extensions of groups / 5.2:
Factorization systems / 5.3:
Reflective factorization systems / 5.4:
Semi-exact reflections / 5.5:
Connected components of a space / 5.6:
Connected components of a compact Hausdorff space / 5.7:
The monotone-light factorization / 5.8:
Covering maps / 6:
Categories of abstract families / 6.1:
Some limits in Fam(A) / 6.2:
Involving extensivity / 6.3:
Local connectedness and etale maps / 6.4:
Localization and covering morphisms / 6.5:
Classification of coverings / 6.6:
The Chevalley fundamental group / 6.7:
Path and simply connected spaces / 6.8:
Non-galoisian Galois theory / 7:
Internal presheaves on an internal groupoid / 7.1:
Internal precategories and their presheaves / 7.2:
A factorization system for functors / 7.3:
Generalized descent theory / 7.4:
Generalized Galois theory / 7.5:
Classical Galois theories / 7.6:
Grothendieck toposes / 7.7:
Geometric morphisms / 7.8:
Two dimensional category theory / 7.9:
The Joyal-Tierney theorem / 7.10:
Final remarks / Appendix:
Separable algebras / A.1:
Back to the classical Galois theory / A.2:
Exhibiting some links / A.3:
A short summary of further results and developments / A.4:
Bibliography
Index of symbols
General index
Preface
Classical Galois theory / 1:
Algebraic extensions / 1.1:
2.

図書

図書
Francis Borceux
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1994  xvii, 443 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 51 . Handbook of categorical algebra ; 2
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Preface
Introduction to the handbook
Abelian categories / 1:
Regular categories / 2:
Algebraic theories / 3:
Monads / 4:
Accessible categories / 5:
Enriched category theory / 6:
Topological categories / 7:
Fibred categories / 8:
Bibliography
Index
Preface
Introduction to the handbook
Abelian categories / 1:
3.

図書

図書
Francis Borceux
出版情報: Cambridge ; New York : Cambridge University Press, 1994  xv, 345 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 50 . Handbook of categorical algebra ; 1
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目次情報: 続きを見る
Introduction
The language of categories / 1:
Limits / 2:
Adjoint functors / 3:
Generators and projectives / 4:
Categories of fractions / 5:
Flat functors and Cauchy completeness / 6:
Bicategories and distributors / 7:
Internal category theory / 8:
Bibliography
Index
Introduction
The language of categories / 1:
Limits / 2:
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