I am very much interested in listening to the history behind the exact sequence. We know that the exact sequence is sequence of objects with morphisms such that image of one morphism equals to the kernel of the next one.
But how did the whole idea start ? .
What is the motivation behind considering the image and kernel equality and linking groups ? .
How did the exact sequences come into play ?.
I want to hear some on some of the above things.
Thank you.
In A History of Algebraic and Differential Topology, Chapter 5, §5, Dieudonné says that Hurewicz introduced exact sequences in 1941.
On the other hand, Weibel in his History of Homological Algebra [1] says that Kelley and Pitcher coined the term “exact sequence” in 1947 [2].
[1] History of Homological Algebra, in History of topology (edited by I. M. James), 1999.
[2] Exact homomorphism sequences in homology theory, Annals of Math. 48 (1947), 682–709.