Lemma 35.35.5. Let X \to S be a morphism of schemes. Let f : X \to X be a selfmap of X over S. In this case pullback by f is isomorphic to the identity functor on the category of descent data relative to X \to S.
Proof. This is clear from Lemma 35.34.6 since it tells us that f^* \cong \text{id}^*. \square
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