2025/04/17 by Clementino, Maria Manuel, Hofmann, Dirk, Prezado, Rui
#06B30 #06B35 #06F30 #18A25 #18F20 #18F60 #22A26 #54B30 #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2504.12965
This paper investigates the interplay between properties of a topological space X, in particular of its natural order, and properties of the lax comma category Top \Downarrow X, where Top denotes the category of topologicalspaces and continuous maps. Namely, it is shown that, whenever X is a topological \bigwedge-semilattice, the canonical forgetful functor Top \Downarrow X → Top is topological, preserves and reflects exponentials, and preserves effective descent morphisms. Moreover, under additional conditions on X, a characterisation of effective descent morphisms is obtained.