Is there an elementary way to define Haussdorf-compactly generated weakly Hausdorff topological spaces in a way that does not need defining topological space first?
Weakly Hausdorff sequential spaces have an alternative cryptomorphic axiomatization as Hausdorff subsequential spaces, which are arguably simpler to define than topological spaces, and have the property that dropping the Hausdorff condition turns it into a quasitopos.
One would hope then that compactly generated k-Hausdorff spaces have a similarly well behaved definition that can skip the usual presentation of things, since the category is very natural. Is there such a presentation?
