Perfect maps are exponentiable - categorically (Q2732026)

The authors provide a purely categorical and moreover choice-free proof of the fact that pullbacks of quotient maps along perfect maps are quotient maps. As applications they obtain the known result that perfect maps are exponentiable in the category \({\mathcal T}op\) of topological spaces, and related new results for the categories \({\mathcal P}os\) of partially ordered sets, \({\mathcal P}r{\mathcal T}op\) of pretopological spaces, and \({\mathcal T}op^2\) of continuous maps.