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.