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.Clementino, Maria ManuelLucatelli Nunes, Fernando2024-10-172024-10-172023https://oa.tib.eu/renate/handle/123456789/16993https://doi.org/10.34657/16015Let Ord be the category of (pre)ordered sets. Unlike Ord/X, whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category Ord//X. In this paper we show that the forgetful functor Ord//X→Ord is topological if and only if X is complete. Moreover, under suitable hypothesis, Ord//X is complete and cartesian closed if and only if X is. We end by analysing descent in this category. Namely, when X is complete and cartesian closed, we show that, for a morphism in Ord//X, being pointwise effective for descent in Ord is sufficient, while being effective for descent in Ord is necessary, to be effective for descent in Ord//X.engeffective descent morphismslax comma 2-categoriescomma categoriesexponentiabilitycartesian closed categoriestopological functorsenriched categoriesOrd-enriched categories510Report