Facets of descent, I

Janelidze, George; Tholen, Walter

doi:10.1007/bf00878100

Cited by 88 publications

(83 citation statements)

References 17 publications

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“…The last equality follows from the fact that the square (1) is a pushout in V (which can be deduced from the property 5 of the commutator in a Maltsev variety), so that [7]. From this it follows easily that the pullback functor…”

Section: Galois Structure Of Central Extensionsmentioning

confidence: 93%

Galois theory and double central extensions

Gran

Rossi

2004

Homology, Homotopy and Applications

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Section: Galois Structure Of Central Extensionsmentioning

confidence: 93%

Galois theory and double central extensions

Gran

Rossi

2004

Homology, Homotopy and Applications

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“…an equivalence of categories) [11]. One can easily verify that Theorem 4.3 of [21] remains valid in the context of the present paper.…”

Section: Effective Codescent Morphismsmentioning

confidence: 68%

Effective codescent morphisms in the varieties determined by convergent term rewriting systems

Samsonadze

Zangurashvili

2016

Tbilisi Math. J.

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It is shown that the elements of amalgamated free products in a variety of universal algebras have unique normal forms if the variety is represented by a confluent term rewriting system satisfying some additional requirements for its signature and rules. Applying this fact it is proved that any codescent morphism is effective in such varieties. In particular, this is the case for the variety of Mal'tsev algebras, the varieties of magmas with unit and two-sided inverses, idempotent quasigroups, unipotent quasigroups, left Steiner loops, and right Steiner loops.2010 Mathematics Subject Classification. 08B05. 08B25, 18C20, 68Q42 Keywords. Variety of universal algebras, normal form for an element of amalgamated free product, confluent term rewriting system, effective codescent morphism.

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“…For example, one may replace the slice category over the object at the "tip" of cocones by a (full) subcategory of it; this is exactly the step from global descent to E-descent [19] and is closely related to the proposals in [11,13] for a weakening of the notion of adhesivity.…”

Section: Conclusion Related Work and Future Workmentioning

confidence: 99%

Being Van Kampen is a universal property

Sobociński¹,

Heindel²

2011

Logical Methods in Computer Science

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Abstract. Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are precisely those diagrams in a category that induce bicolimit diagrams in its associated bicategory of spans, provided that the category has pullbacks and enough colimits.

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Facets of descent, I

Cited by 88 publications

References 17 publications

Galois theory and double central extensions

Galois theory and double central extensions

Effective codescent morphisms in the varieties determined by convergent term rewriting systems

Being Van Kampen is a universal property

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