The Stacks project

Example 6.11.3. Let $X$ be a topological space. Let $A$ be a set. Denote temporarily $A_ p$ the constant presheaf with value $A$ ($p$ for presheaf – not for point). There is a canonical map of presheaves $A_ p \to \underline{A}$ into the constant sheaf with value $A$. For every point we have canonical bijections $A = (A_ p)_ x = \underline{A}_ x$, where the second map is induced by functoriality from the map $A_ p \to \underline{A}$.