Mindblowing fact

Whoops, double post.

interesting, but i believe all that isn't really borrowed from category theory, it is basically the mathematical definition of a function (or endo/iso/epi/whatever morphism).

  On 6/7/2010 at 11:40 PM, GORDO said:

interesting, but i believe all that isn't really borrowed from category theory, it is basically the mathematical definition of a function (or endo/iso/epi/whatever morphism).

I guess that's the problem with category theory, isn't it? All the concepts are generalisations of common concepts in mathematics. Maybe I should've used functors as an example instead.

ehh…

i've got no trouble churning out some proper nested code that's never readable to anyone else, but this maths formula stuff is like an alien language to me.

  On 6/7/2010 at 9:02 AM, ericsosh said:

  Quote

how does one approach category theory?

 

Category theory is used to study mathematical structures and the relationships between them. So it helps to be familiar with different kinds of structures, so you already know of some similarilities between structures, for example: bijections on sets are the same kind of functions as isomorphisms on groups. Category theory deals with this kind of similarities. It can get awfully abstract, but that's why it's fun.

I worked a bit on different kinds of morphisms in algebra this semester, even though I think I still don't know many important properties.

I found out there's a category theory course here too. What did you study before algebraic topology? How long did it take?

  On 6/7/2010 at 4:41 PM, GORDO said:

imo category theory isn't interesting at all, for a glimpse of it study more abstract algebra like module theory.

We proved that every finite abelian group is isomorphic to a direct sum of cyclic groups using modules.

Since I had studied vector spaces before modules, at first I found really odd that some modules can have bases with different cardinality or no basis at all.

  On 6/6/2010 at 8:09 AM, GORDO said:

I've been teaching as T.A. for the past few years, I might get my own course this semester.

Did you always want to teach?

not really, not something I planned it just sortoff happened. I'd rather do research than teach tho, it's ok, i enjoy it mostly but the pay sux.