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Composites of effective descent maps. (English) Zbl 0792.18001

In a category with pullbacks and coequalizers, it is proved that, for any effective descent morphism \(q: E\to X\) and any morphism \(\varphi: X\to B\), descent data with respect to \(\varphi\) are equivalent to descent data with respect to \(\varphi q\). As a consequence, the class of effective descent morphisms is closed under composition.

MSC:

18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18C20 Eilenberg-Moore and Kleisli constructions for monads
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References:

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