Today I was wondering about the axioms given by Bernhard Keller for Cosuspended Categories.
The axioms of a triangle feel very much like exactness, but not quite. The last axiom about the large commutative diagram is particularly quizzical. While I am ok with understanding these axioms I was hoping to ask two questions about them.
1) What was the classical motivation for these axioms? Was there a particular example in mind to conform to?
2) Is there a modern motivating example for these axioms that differs from the classical?
I understand these things much better when I have specific examples to keep in mind, and since I am learning these in a general context, right now that is lacking. I was hoping you all could fill me in.
Thanks in advance!