nLab
(1,2)-topos

Contents

Context

Topos Theory

topos theory

Background

Toposes

Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory

Theorems

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)(1,2)-topos.

The poset of truth values

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

should play the role of the “sub-poset classifier” in PosPos, 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 11:38:54. See the history of this page for a list of all contributions to it.