Some Aspects of Topological Descent

Manuela Sobral ()
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Manuela Sobral: Universidade de Coimbra, Departamento de Matemática

A chapter in Categorical Topology, 1996, pp 97-106 from Springer

Abstract: Abstract The paper deals with (effective) descent morphisms for subfibrations $$\mathbb{E}$$ (X) of the basic fibration T op/X, for topological spaces X and classes $$\mathbb{E}$$ of continuous functions stable under pullback. For a category with pullbacks, we prove the stability under pullback of effective e-descent morphisms for a class $$\mathbb{E}$$ satisfying some suitable conditions. This plays a rôle in relating effective $$\mathbb{E}$$ -descent to effective global descent and enables us to obtain a criterion for effective étale-descent. We also show that the inclusion of the class of effective global-descent maps in the class surjective effective étale-descent is strict.

Keywords: descent data; (effective) descent map; monad; monadic functor; universal regular epimorphism; effective equivalence relation; étale-descent; 54B30; 18A30; 18C20; 18A40; 54C10 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_9

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DOI: 10.1007/978-94-009-0263-3_9

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