Here is the part of the book (user's guide to spectral sequences) I am reading:
I have the following questions about this part:
1- Why we are sure that $k$ has an inverse (the user used $k^{-1}$)?
2- if $d = j \circ k$ why $\ker d = k^{-1}(\ker j)$?
3- Why $k (\ker d) = k'(\ker d/ \operatorname{im} d)$?
4- Why $ k'(\ker d/ \operatorname{im} d)$ is considered as the whole image of $k'$?
Could anyone help me answer those questions please?