From quasitoposes to infinity quasitoposes
I will explain how the general construction of (Grothendieck)
quasitoposes as categories of separated objects can be
generalised, in the infinity setting, to be made relative to
certain stable factorisation systems, the motivating examples
being the ($n$-connected, $n$-truncated) factorisation systems,
(the classical case being $n = -1$, the (epi, mono)
factorisation system). This is joint work with David Gepner,
arXiv:1208.1749.