[FreedomNeocon]

"Natural Transformations" are the closest thing to GOD in Mathematics.

In fact, if you study string theory, you find it is part of "God"

[MaryFromMichigan]

So young...

J

[nuconvert]

pong

[ThePythonicCow]

The best summary of Category Theory I can find is in: Stanford Encyclopedia of Philosophy: Category Theory. Category Theory is an alternative to Set Theory for the foundations of mathematics.

Mathematical foundations are very much like starting off to build whatever you can out of Legos, where you constrain yourself to the most basic and essential minimum kinds of Legos. One starts off with a few axioms which specify that certain Sets or Categories exist. This is just like saying "Let's suppose we have all the 4-bump legos we want; then let's see what we can build."

Read the Zermelo-Frankel Set Theory Axioms You will see things like

1. There's an empty set.
2. If x and y are sets, then the pair {x, y} is also a set.
3. If x is a set of sets, then there is another set which is the union of all the sets in x.

This is just mathematicians saying "suppose we start with these - now what can we build?" It turns out they can build all the familiar mechanisms of mathematics - arithmetic, algebra, calculus, geometry, and so forth. A French group, writing under the name Nicolas Bourbaki, produced perhaps the most famous exposition of mathematics, starting with just basic Set Theory.

In Category Theory, we start out with the basic idea of mappings, or morphisms. We suppose that we have the identity morphism (maps objects to themselves) and that for any two morphisms, we have the composition (if one morphism F maps a to b, and another G maps b to c, then we suppose we also have another morphism H that maps a directly to c. Then, as with Set Theory, we build the rest of mathematics on this foundation.