The Diers spectrum of $U$ is the functor $B^{op}\to Set$ that sends an object $X\in B$ to the set $I$ that indexes the value $(g_i\colon B\to U(A_i))_{i\in I}$ of the left multiadjoint of $U$ at $X$. A morphism $f\colon X\to X'$ is sent to the induced map $I'\to I$ that assigns to $i'\in I'$ the unique $i\in I$ such that $g_{i'}\circ f\colon X\to U(A'_i)$ factors through $g_i$.