Lemma 76.51.1. Let $S$ be a scheme. Consider a commutative diagram of algebraic spaces

over $S$. Let $B \to B'$ be a morphism. Denote by $X$ and $Y$ the base changes of $X'$ and $Y'$ to $B$. Assume $Y' \to B'$ and $Z' \to X'$ are flat. Then $X \times _ B Y$ and $Z'$ are Tor independent over $X' \times _{B'} Y'$.

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