Extended Galois Theory and Dissonant Morphisms
نویسندگان
چکیده
For a given Galois structure on a category C and an eeective descent morphism p : E !B in C we describe the category of so-called weakly split objects over (E; p) in terms of internal actions of the Galois (pre)groupoid of (E; p) with an additional structure. We explain that this generates various known results in categorical Galois theory and in particular two results of M. Barr and R. Diaconescu BD]. We also give an elaborate list of examples and applications.
منابع مشابه
A History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more general categories. Galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...
متن کاملExtensions of Galois Connections
Galois connections play a very important role in the theory of continuous lattices and their various generalizations. (See, for example, [1], [2], [a], [4], [5], [7] and [9].) Morphisms of continuous lattices, as defined in [2], are precisely those upper adjoints of Galois connections which preserve directed sups. In [1] Bandelf and Ernd suggested that the right choice of morphisms for Z-contin...
متن کاملHigher Central Extensions in Mal'tsev Categories
Higher dimensional central extensions of groups were introduced by G. Janelidze as particular instances of the abstract notion of covering morphism from categorical Galois theory. More recently, the notion has been extended to and studied in arbitrary semi-abelian categories. Here, we further extend the scope to exact Mal’tsev categories and beyond. For this, we consider conditions on a Galois ...
متن کاملRight-projective Hulls and Galois Galois Theory
Let N be a bijective measure space. D. Sasaki’s classification of positive definite, globally universal domains was a milestone in homological Galois theory. We show that |O| ≤ K. The groundbreaking work of H. Thomas on contra-arithmetic planes was a major advance. Recent developments in analytic group theory [36, 36] have raised the question of whether Fréchet’s conjecture is false in the cont...
متن کاملConnected and Disconnected Maps
A new relation between morphisms in a category is introduced – roughly speaking (accurately in the categories Set and Top), f ‖ g iff morphisms w : dom(f) → dom(g) never map subobjects of fibres of f non-constantly to fibres of g. (In the algebraic setting replace fibre with kernel.) This relation and a slight weakening of it are used to define “connectedness” versus “disconnectedness” for morp...
متن کامل