\begin{definition}[Definition:Morphism of Ringed Spaces/Definition 1]
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
:$f^\sharp: \OO_Y \to f_* \OO_X$ is a morphism of sheaves to the direct image sheaf of $\OO_X$ via $f$
\end{definition}