New variations on the notion of topos
By André Joyal
The notion topos is a prominent member of a family of notions which includes that of abelian category, of locally presentable category and of higher topos. We propose two new members: the notion of locus and that of para-topos. The category of pointed spaces and the category of spectra are examples of loci. The category of small (weak) $n$-categories is an example para-topos for every $n\geq 1$.