Hegelfags and mathfags pls

>but most likely the adjoint pair
Yes, this is corroborated by the text at the beginning:
"In terms of the corresponding adjoint triple of (co-)reflections and localizations ... In terms of the corresponding adjoint triple of (co-)reflections and localizations "
Now it makes sense that those are modalities, because as the link defines it, nothing, being, necessity, chance, possibility, and impossibility all are considered modalities. Now modal type theory would apparently be concerend with the use of modalities in type theory. However it is still not clear what is the relation between modal type theory and adjoint triples.

Probably though Quillen adjoint triple does look kind of similar, and yes I believe that's also the real point of the author, but what it's trying to do is more than anything to formalize Hegel's "Science of Logic"

apparently the fact that the outer adjoints are full and faithful (that they're bijective between the objects and morphisms) make it possible to induce an adjoint pair "in the codomain of the inclusions" whatever that means, I'm not sure how there would be any inclusions but I guess it could be true. Though it makes sense that a pair is made out of a triple, and it's also meaningful that if you have two bijectives then that means that one can reverse that bijection and hence make an adjoint pair.
And given that it goes from one to the other and back from the other to the one in the adjoint triple (from C=> D, from D =>C and from C=>D) makes the notation for the adjoint triple pretty obvious
Now in this case it is clear that the map are maps of inclusion since the initial and terminal objects are included in H and as one can see the arrow on top and the arrow on bottom both point to the H, so that when transformed perhaps to the adjoint pair both turn out to be adjoint pairs, I imagine. But there is still some ambiguity in the notation as to what the rotated T means below and above the arrows, and how is this adjoint triple related to the empty set or the initial object that is, but both problems are rather the same problem I imagine.
And finally apparently the unit transformation is given by the canonical natural transformation as indicated in section 2. Though it's not clear why it's unique

I'll try it later though I have some other things to do, but just try to develop it from here and don't assume that maths is different from literature.

>formalize Hegel's "Science of Logic"
Isn’t this rather unhegelian?

maybe but just look at this: ncatlab.org/nlab/show/Science of Logic

isn't science of logic unhegelian?

yes
yes

It's category theory, I doubt that most algebraists could differentiate between shit made up on the fly and actual mathematics.

Category theory is pretty specialized, unless he is an algebraist AND somewhat advanced in his studies there is little chance he knows much about it.

Hi

Hey

I am pretty serious about math and while I don't understand it myself, ncatlab is a very respectable resource and I can assure of you everything in the picture and the website has actual, precise meaning and is useful for peopel who study it. Not sure why you are mentioning hegel, who, on the contrary, is a fag whose writings are mostly meaningless fluff. You insult actual mathematics by comparing it to hegel.

Well, am major in math, here's my recommendation
1. Category theory, and just generally foundations in mathematics, we don't care. Foundation is always like that.
2. When we care this particular thing is when "Sheaves", the concept of algebraic geometry become get some importance, and this is very complicated field. There's math professor who don't know anything about it.
3. Maybe CS student who is learning Haskell would be helpful, but, also, he will not know what Topos, generalization of topology, mean
4. Hegel is the most hardest guy i've read when it comes to philo. CoPR was logical, Being and Time was very hard but it felt like topology-kind of logical structure. But hegel. He is literally spewing bullshit to me.
5. Well, assume that CS student know well on adjoint functor. And all undergrad knowledge in mathematics. But.. topology can be easy, but right now in here it's fucked up shit. I'm 90% sure it is high concept in topos via Algebric geometry, I've heard heyting is involved to this. De Rham.
6. Maybe next year I will get full picture on stokes' theorem. De Rham is generalization of that. Think about next boss of final boss.

Did I said recommendation. I'm sorry. I'm sure only less than 1000 people in whole earth can understand full about this article. Seriously.

Stupid

All good?

Sorry. If this is just completely independent to Hegel's hegel-logic, then there is a lot of people who know about this, like 2000000 I guess. I thought this is attempt of connecting hegel-logic and real logic.
Hegel would be most hard one go mathematcian. I would not the only one.

If you give too much on math, you will become "the most logical guy" when attempting to learn philosophy. even very logical one in philosophy become gibberish to mathematician. I experienced that. Ethics especially. Don't even mention postmodernist and Hegel. to me only fitting one was Frege, Hume, and Kripke. even Tractatus looked bullshit-y to me back then. It needs a lot of time to "recover" from that syndrome.

>most hardest

Attached: 1558640150317.jpg (500x322, 16K)

スミマセン desu

what's the doi of the article

I have a degree in math, and I know a few other people who have them from different universities. We generally don't study category theory if at all, and if so usually in a very light setting (like how measure theory might be lightly taught in a class on real analysis).

>Hegel is the most hardest guy i've read when it comes to philo.

Really?

I would be interested to know the purpose of this. I must admit, I am dubious that the meaning represented here does not have a simpler form. I have heard Hegel was purposefully obtuse. This feels a little purposefully obtuse.

Thanks you very much user.

Come on user.

So i should just study category theory and type thoery? I have taken one course in abstract algebra, and what he's writing looks like gibberish

seconding this

It's from Hegel