A (0,1)-presheaf is a presheaf with values in the (0,1)-category of truth values. A 0-truncated (∞,1)-presheaf.
A (0,1)-presheaf on a poset or proset $P$ is an antitone predicate
from $P$ to the poset $\Omega$ of truth values, or equivalently, a monotone predicate
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
so (0,1)-presheaves are just antitones.
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 (0,1)-presheaves on a posite forms a locale.
Last revised on July 22, 2022 at 08:25:18. See the history of this page for a list of all contributions to it.