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The Stacks project

Lemma 79.12.2. Let S be a scheme. Consider a commutative diagram

\xymatrix{ X' \ar[rr]_ j \ar[rd] & & X \ar[ld] \\ & Y }

of algebraic spaces over S. If j is an open immersion, then there is a canonical injective map of sheaves j : (X'/Y)_{fin} \to (X/Y)_{fin}.

Proof. If (a, Z) is a pair over T for X'/Y, then (a, j(Z)) is a pair over T for X/Y. \square

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