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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