## Monday, July 12, 2010

### Future Directions

It is kind of open what I am going to do with this notebook/blog. I don't really know myself. Personally, I prefer TeX as my markup language as opposed to html, which is why I don't write as much as I should.

(Rant: TeX is just so much more convenient! It actually allows me to change notation with the flip of the wrist! For example, consider \let\propersubset=\subsetneq, then I simply use A\propersubset B and if I hate the notation...well, one line of code changed! With html, I have to change everything by hand. Or counters...html has no counter macros, grr...)

It would be nice to "categorify" Bourbaki's work. Take that with a grain of salt! What I mean by this is to be as comprehensive as Bourbaki (I'm reading through his Algebra right now), presenting definitions as e.g. a group object instead of a group, a magma object instead of a magma, etc.

That is to say, present the same material "internalized" in an arbitrary category. So for an example of this, consider the following definition:

Definition 1. A Magma Object consists of an object M in a monoidal category C equipped with a morphism μ:M⊗M→M.

I must confess that such an endeavor is appealing to me, but I might do it in LaTeX (taking advantage of its flexibility).

### Short Summary

I think I will probably end up writing up a cohesive collection of notes — in the spirit of Bourbaki — that is self contained covering all of mathematics (from Set Theory and Category Theory foundations to...whatever!). However, I think I'll TeX it up, and post it online.

(As an aside, there is an interesting project called LuaTeX (there is also LuaLaTeX). There is no memory limits for it, and it has embedded Lua code. Perhaps it would be interesting to use this when writing notes involving numerical calculations?)