Is there a term for the idea that mathematical objects are defined by their relationships?

Question

In a recent Veritasium video discussing Euclid's Elements, Alex Kontorovich comments that Euclid's definitions of primitive objects (e.g. "A point is that which has no part.") are absurd and lead to an infinite regression of definitions. He goes on to say:

You shouldn't have definitions; you should have undefined terms... It's the relationships between the objects that's important, not the definitions of the objects themselves.

(timestamped link: https://www.youtube.com/watch?v=lFlu60qs7_4&t=1042s

Is there an agreed-upon term for the idea that a mathematical object is entirely defined by its relationships to other mathematical objects? I'd like to read more about it, but I don't know what to search for.

Answer 1

In the philosophy of mathematics, the term is structuralism. See here for a survey.

Answer 2

This seems related to extensionality (but not identical).