Why $F^{+}$ is a monopresheaf?

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I'm having difficult in proving that given a site $(C, J)$, then $F^{+}(c) = colim_{R \in J(c)} R $ is a monopresheaf, in the sense that there exists at most one lifting of $R \longrightarrow F^{+}$ to $h_U$ for $R \in J(U)$. Furthermore considering topological spaces, is there an interpretration of the functor ${+}$ viewing $F$ as an étale space? Note that the functor ${++}$ from presheaves over a topological space can be defined picking the sections of the étale space $\coprod_{x \in X} F_x$.

Thanks in advance.