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Another Approach to Topological Descent Theory

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Abstract

In the category T op of topological spaces and continuous functions, we prove that surjective maps which are descent morphisms with respect to the class E of continuous bijections are exactly the descent morphisms, providing a new characterization of the latter in terms of subfibrations E(X) of the basic fibration given by T op/X which are, essentially, complete lattices. Also effective descent morphisms are characterized in terms of effective morphisms with respect to continuous bijections. For classes E satisfying suitable conditions, we show that the class of effective descent morphisms coincides with the one of effective E-descent morphisms.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Coimbra, 3000, Coimbra, Portugal

    Manuela Sobral

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  1. Manuela Sobral
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Sobral, M. Another Approach to Topological Descent Theory. Applied Categorical Structures 9, 505–516 (2001). https://doi.org/10.1023/A:1012082726870

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