[myWindoonn]

Yoneda just says that we may exchange an object for all of the arrows which point to (dually, from) it. This is extremely deep; it is rather surprising that objects and arrows would have such a duality or exchange!

[hutchisonc]

+1. The lemma is trivial not because the result isn't deep but because we have the right definitions.

[Koshkin]

This 'triviality' issue has reminded me of Grothendieck's "two styles in mathematics":

http://www.landsburg.com/grothendieck/mclarty1.pdf

[Koshkin]

Not exactly unexpected conceptually though, given that objects have no intrinsic structure. What may be surprising is that this fact has useful consequences in applications to concrete mathematical objects that do have structure.