FOM: Structures prior to homomorphisms

[Solomon Feferman]

The following quote is from Peter Freyd's book "Abelian Categories", 1964,
p.1:  "It is not too misleading, at least historically, to say that
categories are what one must define in order to define functors, and that
functors are what one must define in order to define natural
transformations."

Not only is it "not too misleading", what other order could these
definitions be put in?

The relation of categories to functors is just a special case of the
general relationship of algebraic structures to homomorphisms.  You can't
define the latter without specifying the former (at least, not
mathematically).