Constant presheaf of sets
= Constant presheaf of sets
{title2=$K_T(U)=T$}
Every restriction is the identity. Its stalk at each point is $T$, and its <étale space of a presheaf> is $X\times T$ with $T$ discrete. It is generally not a sheaf; in particular its value on the empty open set is $T$. Its <sheafification> is the <constant sheaf of sets>.