# Spectral sequences on their own right

I have begun to read a bit about Spectral Sequences. I have been studying some topics of algebraic topology and this "tool" came up from time to time. I didn't need to go deep, but I felt I had to read a bit. Things started to get more delicate, e.g. the Adams S.S., and more stuff. So I wondered (before attempting this), if these things are important in their own right. I guess so, but I wonder what part of mathematics concentrate on them, and what "gadgets" and conjectures exist about them, independently if may be of where you will use them. I would ask for reference, also, thanks in advance.

• I tried to add the reference request tag to your post - is there a relevant related field you also wanted to look at? I'm not familiar with Spectral Sequences, but that sounds a bit like Linear Algebra, while you have mentioned it in algebraic topology and tagged category theory ... – theREALyumdub Sep 28 '18 at 23:45
• I think a lot of spectral sequences can be viewed as special cases of the spectral sequence where $E^2_{ij} = R^i F (R^j G (X))$ and $\bigoplus_{i+j=n} E^\infty_{ij} \simeq R^n (F \circ G)(X)$ - which is a fairly general category theoretic construction relating compositions of derived functors to derived functors of compositions. (Not completely sure about the details of this, though, so I'm not sure I could expand this to a full answer.) – Daniel Schepler Sep 28 '18 at 23:46
• Thanks, interesting viewpoint, I 'll try to check it out – vanmeri Sep 28 '18 at 23:51