He studies about something that doesn't even exist

>he studies about something that doesn't even exist

can mathfag be anymore pathetic?

What do you do all day, OP?

I study algorithm

We give names to things and then see how they relate to each other in n number of dimensions.
Very useful stuff user

>He doesn't know what a Hodge theater is.
mfw

>studies about useless algorithms that doesn't have to do anything with reality

can a programmer be anymore pathetic?

>he is bound by the physical world
You radiate your inferiority, but can't get under my skin, low testo beta physicucks

I can code better programs with my knowledge but you cant do jack shit with your smooth curve or rings or fermat theorem.

He could spend his day complaining about people he doesn't like on the internet

Au contraire, I study things which are underpin the fabric of reality, and yet I am free of how those things are related. I'm living the life.

O H P
H
P
H-hi :3

Hey animebro, how have you been? What sorts of wisdom have you accrued?

>revering a gypsy nigger

I've been fine, thank you. I've been studying algebraic topology, homological algebra and category theory by myself for quite some time now, and on top of this I'm having a course on topological algebra and cosmology to get the remaining credits I need for graduating. I don't know if you remember (and won't feel bad if you don't), but I talked with you about making a master's thesis on the Freyd-Mitchell embedding theorem. I have my advisor who said she accepts my choice of topic, so that's proceeding aswell.

How about you? Any proggress on your work?

If a guy is nice, I don't give a flying fuck if he's a gypsy nigger or any other member of a minority. The internet frees us of the shackles of place and physical existence up to the point that our bodies are needed only for operating the machinery of communication. For a user like the three of us, there are no physical bodies on Veeky Forums.

>he believes "something" "exists"

>he studies if something can exist or not
ftfy

No, I recall our discussion of Freyd-Mitchell! I don't remember what my suggestion was, but I feel like it had to do with characterizing when some sort of converse holds (that sounds funky).

I have been fantastic myself; I am studying differential geometry a la Urs Schreiber's program, and also examining generalized universal bundles. I am developing a generalization of categories such that every higher category has a delooping, not just monoidal categories. With these objects (I call them apparatuses), it's always possible to translate general bundle transformations (between categories or whatever) into morphisms or paths in the underlying spaces, and in this sense it is sort of like higher category theory and homotopy after being stabilized with respect to twisting (in the sense of twisted cohomology).

I'm just a sophomore, so this has all been self-study. I am working with a professor at a nearby university on his research right now, though. He feels I will be able to get into the graduate program early, without a bachelor's degree. Life is good, user!

You suggested looking into when the embedding is a localization. I think it's a good idea to include it in the text. The structure I have in mind is:
>the required category theoretical objects per se and the needed lemmas regarding the objects
>defining abelian categories and showing R-mod is one
>defining functors and the desired properties, and proving the stuff regarding functors needed later
>defining smallness, proving the main theorem and using it to prove some diagram lemmas in a general abelian category
>defining localization, finding suitable conditions for the embedding to be one and proving maybe something requiring the localization
It's nice that you remembered.

Your stuff sounds interesting. Do you still call it hodology? Just one thing I'd like to stress: please call them apparati instead of apparatuses (both are correct but it's like people vs persons)! You being a sophomore means you are one talented guy.

>algorithms
>programming exclusive
literally lmaoing@ your life right now

Math is like a 2D waifu. She isn't real, but that's what makes her so pure. Whereas real science is a disgusting 3DPD.

Ohhh, that's right! This question still piques my interest a great deal. It's awesome that your advisor thinks it's a nice avenue of discourse!

I have defined the category of hodological spaces fully and shown it to form a cohesive topos; the next step is to see if it's a sheaf topos and then figure out the site of definition. That would be nice. I also want to find semantics for the dual algebras.

I originally called them apparati, but it sounded sort of goofy. I'll have to switch it up.

I like the outline of your thesis, it sounds well-structured! Have you found anything interesting yet to detect when such embeddings into RMod are localizations? I feel in my gut that it will be related to the ideals of R and some kind of condition showing that the subcategory is a filter induced by some ideal. Best of luck! Keep me posted.

please stop avatarfagging

>please call them apparati instead of apparatuses (both are correct but it's like people vs persons
You are trying to look super smart and educated, but failing miserably. The plural of 'apparatus' is 'apparatus' in Latin. Are you one of those fags that say 'topoi' instead of 'toposes' even though the etymology is very different?

Yes, I find it interesting too. Even though my courses are rather easy at the moment, I still have to do a lot of work on them, I have a job to keep me alive, and would like to have some time to do my own stuff, so looking into it with more detail may take some time to happen. I'll inform you when I know more (and see your posts).

It sounds like you are making nice progress. It's hard to comment much more on this without seeing your work, but I know I wouldn't post it just because some random user I've talked a few times before with asked to see it.

Disregard my "advice" on apparati. It seems I unintentionally sabotaged your vocabulary.

I checked it, and it seems you are right about that. I admit my mistake, I should have checked it before assuming too much. About trying to look super smart and educated, nope. It's just that seeing certain words being written just feels bad. Apparatuses, toposes, simplexes, etc. It makes no difference if they are correct or not, it just feels wrong in some aesthetical sense.

I was wrong about it too, user. We're all gonna make it.

(And, I say topoi. Toposes sounds super dumb.)

Indeed we are. The best of luck with your pursuits!

Without rings you wouldn't have your precious public key crypto systems