Frege's logic and Category theory

[timelets]

If I remember my logic classes correctly, Frege started a revolution in logic by analyzing identity statements like "The morning star is the same as the evening star." In terms of the Category Theory this statement would mean that some arrows commute. Right? Then, what would be a category (objects and arrows) we can use to express Frege's thinking?

upd: it would be even more interesting to diagram the process of discovery; that is, how did the Babylonians discover that expressions about the two stars denoted the same star?