Seeing too many threads about category theory lately, so let's just get it all over with right here and now.To everyone who doesn't like category theory, unload your genuine criticisms of the field related solely to the field itself, and set aside feelings about the actual people working in it.(I work in Topos Theory btw. So remain chill Catfags)
emily riehl has very sexy bags under her eyes but also maybe she should sleep more
>>16928501the only question category theory answers is, "how can express the fact that the 1st isomorphism theorem for rings is kinda the same as the 1st isomorphism theorem for groups, and then try to generalize more?". And universal algebra did it better>inb4 homological algebraNo motivation or applications besides the "applications" in topology that were contrived by homological-algebra specialists>inb4 "category theory as foundations"baby-duck syndrome. usually, they committed themselves to the idea before ever seeing a basic grad course in logic; and the rest, either grandiose maniacs, or cynical grant-chasers, trying to hocus-pocus the committee. Both set theory and type theory are much easier to understand and explain, especially the "why"Mac Lane's book is a good read though
>>16928767Indeed. In truth one cannot romanticize category theory too much, despite its uses. I enjoy the path I've taken because I set myself up to appreciate the full picture in which my field exists in the backdrop of, but I do not treat it as a messiah. The best thing about category theory and its associated areas is the fact that despite its low barrier to entry, it has a high barrier to competence; this visibly exposes those who make me look bad for my choice of work.
>>16928501Over time I'm more and more convinced that Grothendieck wasn't a category theorist in the sense you might give to that expression today. Just look at what he wrote in the Tohoku paper, or SGA4 where the topoi are introduced. The usage of category is merely the one of a convenient language, instead of drowning a notion under layers of obfuscating buzzwords before studying it, with the false pretense of generalization.Also and unless I'm mistaken (I had read this somewhere but an actual source would be pretty much enjoyed here if anyone has one): the definition of a sheaf over a topological that is used by everyone today is from Grothendieck and not Leray (while the latter is their inventor, he only considered sheaves of modules and the conditions involved closed sets, not open sets): if this true then it is remarkable because the heaf notion (soon to be generalized into the topos-theoretic one) is already incredibly illuminating.Grothendieck was complaining throughout "Recoltes et Semailles" how his work has been misrepresented, I'm afraid he was too much right in that respect.
>>16929205I fucking know right? How did we get from a tool subordinate to algebraic geometry and topology, to a literal fucking school of schizophrenic witchcraft?
>>16929208>to a literal fucking school of schizophrenic witchcrafthttps://youtu.be/jD4-xxR6GRo
>>16929260btfo namefag shill
>>16929205Yes, we use Grothendieck's definition. Yes he complained about being used as a pawn by covert kabbalists seeking to subvert mathematics and turn it into schizo jewish mysticism (which is why khazars = ashkenazim "dominate" in many areas today, able to "prove" results which are unverifiable and vouchsafed by a "sanhedrin" consisting mainly of prominent members of their tribe and a few shabbos goyim). Grothendieck, himself of khazar stock, realized he was manipulated but couldn't do anything about it, and so retreated to the mountains.If you actually look at Grothendieck's writings (his own, not those of his "school" who hijacked what he was doing and turned it into mathematical esotericism), Grothendieck actually despised abstracism and sought to find proofs of results through subtle, "soft" observations on their structure (e.g. motives). His dream was that there should be a category called motives which carries the information of all mathematical structures in their clearest, most primitive forms, and that there should be functors from this category to all others explaining why all theorems are true (they are just complicated manifestations of these rather simple motivic structures). Many of Grothendieck's contributions to math amount to realizing that there is deeper structure behind proofs of known results (e.g. Riemann-Roch, Leray spectral sequence) allowing him to simultaneously vastly generalize them as well as drastically simplify the their proofs. Grothendieck has been overhyped because he was being used, unwittingly unlike Einstein in physics, as a means to bring about a "jewish revolution" in mathematics, giving jews an entrypoint into positions of prominence and thus to continue their program of subverting all of mathematics and science. But Grothendieck himself was not a mystical idiot kabbalist. He had real ideas even if he wasn't able to carry them out and even though he wasn't as great as he is made out to be by the establishment.
>>16929451The tranny's are seething in other cat threads. Denialism doesn't get them anywhere. Pissing and shitting themselves and calling us pseuds doesn't get them anything but extra goyim cookies.
>>16928659Be careful what you say; the rest of the board might hear you.
>>16929440https://youtu.be/FPr1xLaNA_Y>>16929451>schizo jewish mysticismNumber Theory? Why yes, it hold all the way to the bottom with equations like e=mc2.
>>16929776BTFO shill>>>/mu/You're lucky the jannies can't do anything about your ass.
>>16929778>BTFO shillLol. My thesis was on Number Theory specifically...yes. I shill the fuck out of Number Theory. It is the direct connection to physical measurements (Physics itself). Where the whole units come from, including 2 for squared, and again for multiplication(ish).[Would you like to know more?]
>>16929785I'm talking about your fucking video imbeds. You can talk about number theory without fucking /mu/nting everywhere.
https://youtu.be/IMeVhhJ7QGw>>16928501>category theory, unload your genuine criticisms of the field related solely to the field itselfNot irriducable, not full axiomatic yet, by definition. Like Combinatorics.>>16929451>schizo jewish mysticismThe closer you begin to unify all of this, the more it becomes "magic", hyper incongruent dimensional exchanges/maths, because human scale things are correlating at essentially down to 0th dimensional interactions, so "lines/folds/geometries" in their interactions is whats measured for reference to all the rest.People have been studying it long before the Ice Age...100,000 years at least, but revords before then are sparse.
>>16929787>without fucking /mu/nting everywhereIts a test.Like birds, if you fail to hear the call you are self declaring something invertedly...you hand is flat and I can see your cards.Post a song, it will reveal more to me about your knowledge in Mathematics than anything you discuss about the topics could.
>>16928501>In mathematics, a topos is a category that behaves like the category of sheaves of sets on a topological space.Only closed sets? All sheaves eventually converge into a single point...in reality.>set aside feelings about the actual people working in itWar has been declared.https://youtu.be/Hf8yZOfVLMw
>>16928501I am unwillingly forced into it because it is the only system with the terminology to express what I am working on.>>16928767Grandiose maniac. That's the one.
>>16929778>You're lucky the jannies can't do anything about your ass.On one of the alt-Chans they geolocked whole countries to stop me. They knew I was using a VPN and they *still* locked them. Baffling.>>16930295>unwillingly forced into itI love Catagory/Set/etc Theory, very handy tools for many things, its just at a certain level it becomes decoherent without irrationals/transcendentals, then its easier to describe it Dimensionally.
Look at this thing, it shits out a massive code every tick, thats one slice at one dimension.
