\begin{definition}[Definition:Morphism of Ringed Spaces/Definition 2]
Let $\struct {X, \OO_X}$ and $\struct {Y, \OO_Y}$ be ringed spaces.
A '''morphism of ringed spaces''' from $\struct {X, \OO_X}$ to $\struct {Y, \OO_Y}$ is a pair $\struct {f, f^\sharp}$ where:
:$f : X \to Y$ is continuous
:$f^\sharp: f^{-1} \OO_Y \to \OO_X$ is a morphism of sheaves from the inverse image sheaf of $\OO_Y$ via $f$
\end{definition}