Dan Piponi
On 8/15/07, Dan Weston
wrote: "You too could have invented Universal Algebra and Category Theory". I nominate Dan Piponi to write it and eagerly await its release!
I've already started on it. Well, that's not the exact title and subject. And as an example I'll probably use the definition of tensor product that I linked to, not the even more compact and elegant one that you just gave.
I'm a strong believer that lots of (but not all) tricky looking mathematics is just fancy language for intuitions that people already have. I suspect that most computer scientists already have much of the intuition behind the idea of a universal property, and that it is in fact easier to grasp for a computer scientist than a mathematician.
-- Dan
Some universal properties (initial algebras and final co-algebras) are covered in Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire (1991) (http://citeseer.ist.psu.edu/meijer91functional.html). And of course there's Wadler's Theorems for Free. Dominic.