, ,

Of course, if X itself happens to be small, we still have two aspects: a property of indices is the same as a list of values h : IV for example, the map [(1, blond), (2, red), (3, blond), (4, black)] may be a record of composing two maps through some set X of actual people, whereby we sample I people among X, then observe their hair color; from this map alone (i. e. without further investigation, recorded by like maps) we can’t tell―and it might be crucial in a criminal investigation―whether the first and third persons were the same or merely had the same hair color.

(Lawvere & Schanuel, Conceptual Mathematics, Session 6.3)