Contents

topos theory

# Contents

## Idea

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

## Examples

###### Example

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.