Abstract
Methods of internal-category theory are applied to show that the split epimorphisms in a category C are exactly the morphisms which are effective for descent with respect to any fibration over C (or to any C-indexed category). In the same context, composition-cancellation rules for effective descent morphisms are established and being applied to (suitably defined) locally-split epimorphisms.
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Janelidze, G., Tholen, W. Facets of Descent, II. Applied Categorical Structures 5, 229–248 (1997). https://doi.org/10.1023/A:1008697013769
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DOI: https://doi.org/10.1023/A:1008697013769