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It seems like Paul Romer makes a certain mistake in his approach to the theory of innovation. He assumes that characteristic function ("the recipe") is given, while it has to be discovered. In short, the set of elements is the initial object, not the terminal one.
Maybe we can think of the set of elements as the initial object, while the free group generated by it represents the terminal object.
E.g. printed book vs handwritten book (different terminal objects built using different initial objects.)
Maybe we can think of the set of elements as the initial object, while the free group generated by it represents the terminal object.
E.g. printed book vs handwritten book (different terminal objects built using different initial objects.)