G.A.N.

I've been spending some time studying generalized abstract nonsense (sometimes called "category theory" by its practicioners). In fact, I think my paper for the summer will end up relating generalized abstract nonsense to something in algebraic topology. After spending all day dealing with "things" like "metatheorems" or functors that are sometimes faithful and often forgetful, one occasionally needs to step back and gain some perspective. Here are a few choice descriptions of the subject from the masters, which supply just that.

"A direct treatment of categories in their own right appeared in Eilenberg-MacLane [1945]. Now the discovery of ideas as general as these is chiefly the willingness to make brash or speculative abstraction, in this case supported by the pleasure of purloining words from philosophers: "Category" from Aristotle and Kant, "Functor" from Carnap, and "natural transformation" from then current informal parlance."

--Saunders MacLane, "Categories for the Working Mathematician," pg. 29-30.

"As for the proof... well, these diagrams are so natural that one can hardly imagine it any other way!"

--J. Peter May, in lecture the other day.

"No, this isn't category theory. This is real Mathematics."

--Mitya, in lecture the other day.