Good morning,
I am asking a question about the fact that a short exact sequence in an abelian category induces a long exact sequence in cohomology. I believe I can show this in the case, for instance, of abelian groups, as I can work with concrete elements and chase diagramm.
I read, that we can use an embedding theorem, and work as if it was the categorie of A-module, and so the proof I got is satisfying.
Anyway, I would like to know if it exists a proof showing the existence of the $\delta$-map without using elements of objects, ie using only the axioms and properties of abelian categories.
Thank you.