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Jan 20, 2015 at 10:43 comment added user43326 To add to the comment by @AlexDegtyarev the answer to 2) is that the map "f_H on the infinity page" is the associated graded map of $f_J$. This is always the case when a spectral sequence converges.
Jan 19, 2015 at 21:44 history edited Anthony Conway CC BY-SA 3.0
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Jan 19, 2015 at 21:15 comment added Alex Degtyarev All "natural" things are natural. For a cellular map this is even obvious, as you get a map at the level of complexes.
Jan 19, 2015 at 20:44 history asked Anthony Conway CC BY-SA 3.0