Is it worth it that I take it as a class? I'm a last year undergraduate.
Did manifolds become boring once we learned they can all be embedded in R^n? No! In fact the exact opposite is true -- manifolds were originally interesting precisely because they allowed you to get rid of the ambient space!notice that freyd himself says the main result in the subject at the time was the theorem that all abelian categories can be viewed as subcategories of the category of abelian groups. which pretty much took the fun out of them. i.e. how do you persuade people of the generality and power of axiomatic euclidean geometry when the only euclidean geometry is R^2?
(we'll see if we can wake hurkyl up again.)
In Cat, yes: adjunctions are pairs of adjoint functors (together with their units).what is an adjunction? adjoint functors?
That is one aspect of it, and the one most people seem to focus on. But there is another side to category theory, in that you can define richer structures than you can with set theory.to me the main point of category theory is that one should always think not merely in terms of spaces but in terms of maps between spaces.