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Feb 9, 2010 at 22:57 history edited Qing Liu CC BY-SA 2.5
Fix a hypothesis.
Feb 9, 2010 at 22:02 comment added Emerton Do you need to assume that $Y \to X$ is surjective? Otherwise, if $Y$ was an open subset with non-empty complement, and $Z\to X$ was any map with image landing in the complement, the fibre product would be empty, hence have all possible properties, but $Z \to X$ could be quite bad.
Feb 9, 2010 at 21:23 history answered Qing Liu CC BY-SA 2.5