Lemma 77.12.3. Let $B \to S$ as in Section 77.3. Consider a morphism $f : (U, R, s, t, c) \to (U', R', s', t', c')$ of groupoid in algebraic spaces over $B$. Then pullback $f^*$ given by

$(\mathcal{F}, \alpha ) \mapsto (f^*\mathcal{F}, f^*\alpha )$

defines a functor from the category of quasi-coherent sheaves on $(U', R', s', t', c')$ to the category of quasi-coherent sheaves on $(U, R, s, t, c)$.

Proof. Omitted. $\square$

There are also:

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