Special reflexive graphs in modular varieties

Gran, Marino; Rosický, Jiřı́

doi:10.1007/s00012-004-1876-y

Cited by 3 publications

(2 citation statements)

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“…Since C is a Birkhoff subcategory in Eq(C), thanks to Theorem 3.5 the adjunction (2) gives rise to an admissible Galois structure. P Example 5.2 When V is a Mal'cev variety the category Gpd(V) of internal groupoids in V is a Mal'cev variety as well ( [12,20]); therefore Eq(V), that is a full reflective subcategory of Gpd(V) closed in it under subobjects, turns out to be a quasi-variety in a Mal'cev variety. In this situation the effective descent morphisms in V are exactly the regular epimorphisms, and then (Eq(V), V) gives rise to an admissible Galois structure by Proposition 5.1.…”

Section: Coverings Of Internal Equivalence Relationsmentioning

confidence: 99%

“…Let us observe that the theory of central extensions can not be applied in the study of the Galois structure¯ 2 , since Eq(C) is not exact, in general. Particularly interesting is the case when C is a Mal'cev variety, because in this case Eq(C) is a quasi-variety in the Mal'cev variety Gpd(C) of internal groupoids in C ( [12,20]). As a last application we consider the Galois structure¯ induced by the following composite adjunction:…”

Section: Introductionmentioning

confidence: 99%

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Admissible Galois Structures and Coverings in Regular Mal’cev Categories

Rossi

2006

Appl Categor Struct

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Given a regular Gumm category C such that any regular epimorphism is effective for descent, we prove that any Birkhoff subcategory X in C gives rise to an admissible Galois structure. This result allows one to consider some new applications of the categorical Galois theory in the context of topological algebras. Given a regular Mal'cev category C, we first characterize the coverings of the Galois structurē 1 induced by the subcategory C Ab of the abelian objects in C. Then we consider C as a subcategory of the category Eq(C) of the equivalence relations in C, and we characterize the coverings of the corresponding Galois structure¯ 2 . By composing the Galois structures¯ 1 and¯ 2 we obtain the Galois structure¯ induced by C Ab as a subcategory of Eq(C). We give the characterization of the¯ -coverings in terms of the coverings of¯ 1 and¯ 2 .

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Section: Coverings Of Internal Equivalence Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%