/sci/ - Science & Math

>>12715220
Whenever you some diagram result that you can express using commutativity and exactness, and it holds for all module categories, then it holds for all abelian categories. Can you formulate splitting using only those two? Yes you can, actually. It is just a commutative triangle in which one side is the identity. However, this would require two separate diagrams whereas the 5-lemma would be one commutative diagram and several exact sequences. This is probably the reason why it doesn't have to hold, too many diagrams at once! It would probably work if [math]A_*[/math] was acyclic. Assuming that [math]\partial_n(b) \in A'_{n-1}[/math] would then give you an [math]a \in A_n[/math] such that [math]f_n(a) = b[/math]. If then [math]b = q_n(c)[/math], this forces [math]c = 0[/math]. Then my dumb idea would actually work out as you would always have [math]\partial_n(c) \in C'_{n-1}[/math]. Sorry about that.

>>11785816
AAARGH! AW, SR, TB, EY I meant.

>>11785823
>Should I give up on mathematics?
If you have no real motivation, then yeah. Otherwise no.

>>11772418
>(Actually, I think I didn't even make the point he/she/xe was a person)
You will probably be replied how the anon just helped with your ignorance or something. Happened to me when I mentioned Bourbaki in a non-personal way.
>there's texts on topology without LEM and the prove are hard as far as I could tell. Things just get cumbersome there
LEM is a tender lover when doing topology, and I can believe that one will miss his touch when trying to do anything without him. Okay this point is not in the complement so it must... oh wait no LEM,
>So I think the Lie theory will look more like algebra and less like differential geometry.
This seems like a natural consequence of dropping a lot of topological aspects by necessity. The fragile stuff most likely occurs when it is time to start embedding the structures into bigger ones. Is there even any reason to assume all the enveloping algebras would exist?

>>11772442
>Does anyone here do 8+ hours a day?
I'm a workaholic and can easily do 8-10 or more a day with a few breaks.
>if I am self studying should I be doing every exercise at the end or the chapter or just enough to feel like I have understanding?
Do most, proceed, return if necessary.

>>11757925
Exactly. Isn't life just cruel?