Example 1

Let B be a topological space, let $(E, p)$ and $(E', p')$ be B-spaces and let $f: E\rightarrow E'$ be a B-morphism. For every open subset U of B, define the mapping $f_U:\mathscr{S}(U; E)\rightarrow \mathscr{S}(U; E')$ by $f_U(s) =$ $f\circ s$. The family $\mathscr{S}(f) = (f_U)$ is a morphism of presheaves from $\mathscr{S}(B; E)$ into $\mathscr{S}(B; E')$. If $(E'', p'')$ is a B-space and $g: E'\rightarrow E''$ is a B-morphism, one has $\mathscr{S}(g\circ f) =\mathscr{S}(g)\circ \mathscr{S}(f)$.