Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Lucatelli Nunes, FernandoPrezado, RuiSousa, Lurdes2024-10-172024-10-172023https://oa.tib.eu/renate/handle/123456789/16991https://doi.org/10.34657/16013For any suitable base category V, we find that V-fully faithful lax epimorphisms in V-Cat are precisely those V-functors F:A→B whose induced V-functors CauchyF:CauchyA→CauchyB between the Cauchy completions are equivalences. For the case V=Set, this is equivalent to requiring that the induced functor CAT(F,Cat) between the categories of split (op)fibrations is an equivalence. By reducing the study of effective descent functors with respect to the indexed category of split (op)fibrations F to the study of the codescent factorization, we find that these observations on fully faithful lax epimorphisms provide us with a characterization of (effective) F-descent morphisms in the category of small categories Cat; namely, we find that they are precisely the (effective) descent morphisms with respect to the indexed categories of discrete opfibrations -- previously studied by Sobral. We include some comments on the Beck-Chevalley condition and future work.engCauchy completionslax epimorphismseffective descent morphismsfully faithful morphismsenriched categoriessplit fibrations510Report