Yes, I like that too! That principle eventually becomes the Yoneda Lemma in category theory. I really like Tae-Danae Bradley's highly readable blog posts explaining this:

* [The Yoneda perspective](http://www.math3ma.com/mathema/2017/8/30/the-yoneda-perspective).

* [The Yoneda embedding](http://www.math3ma.com/mathema/2017/9/6/the-yoneda-embedding).

* [The Yoneda lemma](http://www.math3ma.com/mathema/2017/9/14/the-yoneda-lemma).

The "Yoneda perspective", in her words, is that

> An object is completely determined by its relationships to other objects.