The notion of *(1,2)-topos* should be the notion of higher toposes among (1,2)-categories or 2-posets.

The (1,2)-category Pos of posets and monotone maps should be the archetypal $(1,2)$-topos.

The poset of truth values

$\big( \bot \to \top \big)
\;\in\;
Pos$

should play the role of the “sub-poset classifier” in $Pos$, the (1,2)-analog of the subobject classifier in a 1-topos.

Here, morphisms into it classify monic fibrations of posets, namely sieves (e.g. Exp. 9.26 here)

**flavors of higher toposes**

Last revised on August 25, 2021 at 15:38:54. See the history of this page for a list of all contributions to it.