Category theory- Historical aspect of universal property

Question

In many fields, category theory is an important tool for problem solving, especially in algebraic topology. When I studied algebraic topology, one of the most useful and important things was the universal property of objects (in $Grp$), i.e free product, free product with amalgamation, abelianization and etc'.

My question is, in historical aspect, what was the first thing to get discovered, and what was the first need? the need of universal property, or the need of these objects?

Thanks in advance.

Answer 1

As Eilenberg and Mac Lane state in their original article introducing category theory, the reason to define categories is to define functors, and the reason for defining functors is to define natural transformations. So, the need was the inherent 2-categorical computations in homological algebras. The need was to develop the 2-categorical language. As far as I know, the characterisation of objects via their universal property, and the usage of that in practice, e.g., the Van Kampen theorem, came later.