Contents

(0,1)-category

(0,1)-topos

topos theory

# Contents

## Idea

A (0,1)-presheaf is a presheaf with values in the (0,1)-category of truth values. A 0-truncated (∞,1)-presheaf.

## Definition

A (0,1)-presheaf on a poset or proset $P$ is an antitone predicate

$F:P \rightarrow \Omega$

from $P$ to the poset $\Omega$ of truth values, or equivalently, a monotone predicate

$F:P^\op \rightarrow \Omega$

from the opposite poset of $P$ to $\Omega$.

More generally, for a poset $S$, a S-valued (0,1)-presheaf on $P$ is just an antitone

$f:P \rightarrow S$

so (0,1)-presheaves are just antitones.

## (0,1)-category of (0,1)-presheaves

The (0,1)-category of a (0,1)-presheaf on a (0,1)-site forms a (0,1)-topos. In traditional order theoretic language, the poset (or proset) of a (0,1)-presheaf on a posite forms a locale.

Last revised on May 5, 2021 at 01:15:45. See the history of this page for a list of all contributions to it.