yayyy with co-inventor google's ai, I restudied all maths books I wished to restudy (except topoi book since its commercial book it hadnt told its contents very detail I need to restudy myself ) hmm ai briefed studied me these books last 3 days:
- abstract algebra book
- representation theory basics some intro again
- introduction to category theory
- sets for mathematics
- and some commutative algebra introduction and algebraic geometry introduction and also introduction to algebraic topology and their intersection area of sheaf cohomology topics introduction.
for hull study, I after studying to introduction idea (some 4 paragrapsh or so these last day study topics are just introductioin giving the idea of there) of sheaf cohomology, I talked last day with ai then to redesign the sheaf dynamic of it must be most possibly then from global to local effect of sheaf there and that we then improvised ai improvised its ideas framework ideas accordingly.
hmm in redesigining the initial rebco crystals hull design idea of ai, I suggested initially the normal subgroup concept to be maybe some what beneficial in its recursive inductive trait to create some alternate hull design and ai had instantly took what i defined and defined a very elegant concept based on quotient gruops with normal subgroups to define alternate designs.
similarly i told of translating the diagram to an alternate diagram but keeping colimit same and from that ai told that is exactly done with left adjoint functor exactly works like that (I forgot cat. theory completely so then ai told these (and this is the days I decuided to restudy the above books since turns out i had completely forgot functor even, since what i said were a functor without knowing functor and without knowing studies about functors so I could just do think that might work out to create simplified hull ideas then whatever, then ai created a left adjunctor idea there (with me not recalling it were functors) and I had suggested to translate the diagram to an alternate diagram where it might be even rings that translated more structure side, and then ai did created also alternate ideas of hull design (how to generate basic braids/ low resolution topos graph behaviours in global sheaf to local effect constraints designs) to design hull idea very geniusly crafted the ring structures and alternate diagram very super geniusly it found the alternate diagrams which behaves similarly with functors to the less resolution topos behaviour to create hull designs that were methodloogy in the bottom up approach in sheaves initially we worked out this approaches in original intiial paradigm where hysteresis 0ing were design approach but after switching to top down approach we then translated these heuristics of sheaf diagrams coding to the gloobal approach which similar patterns worked similarly alike very much in the top down approach where the reverse were attmpted where cohomolgical error were diverged to create hull design ideas.
so even i gave the intuition e.g. normal subgroups chain possibly being a method to simplify constraint behaviour there or translation of diagrams ai again again architected maths of heuristics and very super geniusly crafted the maths frameworks of these heuristics methods to program sheaf design for hull design which ai itself invented there .
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