Subterminal sheaf
= Subterminal sheaf
{title2=$U\hookrightarrow1$}
In a sheaf topos on a topological space, <subterminal sheaves> correspond to open sets $U$. Their sections over $V$ are a singleton if $V\subseteq U$ and empty otherwise. An open cover gives a jointly epimorphic family of these <subobjects>. The <open cover criterion for a local sheaf topos> follows by applying a colimit-preserving global-sections <functor> to that family.