Definition 6.25.3. Let $(f, f^\sharp ) : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ and $(g, g^\sharp ) : (Y, \mathcal{O}_ Y) \to (Z, \mathcal{O}_ Z)$ be morphisms of ringed spaces. Then we define the composition of morphisms of ringed spaces by the rule

$(g, g^\sharp ) \circ (f, f^\sharp ) = (g \circ f, f^\sharp \circ g^\sharp ).$

Here we use composition of $f$-maps defined in Definition 6.21.9.

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