## 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

### Keywords:

effective descent morphism; descent data
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### References:

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