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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.

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    This is not an answer. But here is a link you might find useful: http://www.math.uiuc.edu/K-theory/0245/. Check out the pdf file.2012-05-11
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    While the concept of an exact sequence is purely algebraic, I dare guess that the origin is from topology/analysis/differential equations. At least yours truly first encountered the word "exact" during an elementary course on differential equations. See [this.](http://en.wikipedia.org/wiki/Closed_and_exact_differential_forms) I'm no historian, so my impression may be false, and only reflects the order in which I was exposed to various parts of math.2012-05-11
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    Weibel has some remarks about the history of exact sequences in Chapter 1 of _An introduction to homological algebra_.2012-05-11
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    Sir, Can you tell any motivation behind the kernel image equality ?. Why one needs to consider that ? @ZhenLin2012-05-11
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    IMHO the first time a keen student encounters the kernel image equality is with theorems like (in $\mathbf{R}^3$) *The curl of a vector field vanishes, iff the vector field is the gradient of a function* and *the divergence of a vector field vanishes, iff the vector field is the curl of another*. Of course, these are just reinterpretations of the vanishing of certain de Rham cohomology groups, but they do show up many times, when learning vector analysis. See Poincaré Lemma (in the link of my previous comment).2012-05-11

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