Abstract
The paper deals with (effective) descent morphisms for subfibrations \(\mathbb{E}\) X of the basic fibration Top/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 \(\mathbb{E}\)-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.
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Partial financial support by Centro de Matemática da Universidade de Coimbra is gratefully acknowledged.
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Sobral, M. Some aspects of topological descent. Appl Categor Struct 4, 97–106 (1996). https://doi.org/10.1007/BF00124118
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DOI: https://doi.org/10.1007/BF00124118