Yoneda Philosophy and Relationality

"The idea underlying the Yoneda results is like this. In the most general sense, it might be regarded as saying something like

To understand an object it suffices to understand all its relationships with other things.

Or, to say it in another way,

If you want to know whether two objects A and B are the same, just look at whether all the ways of probing A with other things (or, dually, probing other things with A) is the same as all the ways of probing B with other things (or, dually, probing other things with B)."

Daniel Rosiak in Sheaf Theory through Examples