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Apr 28, 2015 at 3:02 comment added Eric Wofsey @QiaochuYuan: Yes, I would have assumed that, but the phrase "monotone with rank" suggested otherwise.
Apr 28, 2015 at 3:01 comment added Qiaochu Yuan I was already interpreting the second condition to mean "a monomorphism from the image of $f$ to the image of $f'$ compatible with the inclusions into $y$," but it's nice that that extra bit is unnecessary.
Apr 28, 2015 at 2:56 history answered Eric Wofsey CC BY-SA 3.0