Definition:Morphism of Ringed Spaces/Definition 1

Definition
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 $f$