$\xymatrix{ X'' \ar[d] \ar[r]_ g & X' \ar[d] \ar[r]_ f & X \ar[d] \\ S'' \ar[r] & S' \ar[r] & S }$

be a commutative diagram of ringed spaces. With notation as in Lemma 17.27.12 we have

$c_{f \circ g} = c_ g \circ g^* c_ f$

as maps $(f \circ g)^*\Omega _{X/S} \to \Omega _{X''/S''}$.

Proof. Omitted. $\square$

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