There is a trend in mathematics towards reasoning without elements if possible (coming from category theory, I presume). I see the appeal and want to learn how to argue avoiding the use of elements, but in our lectures this isn’t done. (At least not to the extent that I think is possible, and instead, more traditonal arguments are favored.)
I’m a bit of a lazy person, so I won’t work through formal introductions to category theory – although I have basic knowlegde of categories and I’m not reluctant to look up a particular concept or theory.
So I’m looking for good, instructive sources for learning arguing without elements, something focusing on problems and how to approach them – maybe even a documented collection of element-free proofs for common results. Are there any?