yep been reviewing today introduction to cat. theory then would proceed with sets for mathematics book but then had been tired after finishing cat. theory introduction and needed to rest a while then now would try to finish the sets for mathematics book.
hmm then tomorrow would try to finish the topoi book brief of ai. (which some most more than half of chapters before studied to) then would at that moment would do a brief restudying to topology and differential geometry concepts basics. then would proceed with sheaf topics studying and homological/cohomology algebras alike topics and then at that time would study to commutative algebra topics.
to design additional math methods other than which utilizes freegroups and normal subgroups concept for hull design, would need to complete these topics studies alike to define alternate math diagram functor patterns which keeps the colimit but is utterly more high resolution level. hmm normal subgroups (quotient groups method) is a nice method to remove commutator clashes. (and that but that being suggested by me to ai (in creating alternate designs than rebco study initials 2 days ago) but I had not exactly suggested that trait of quotient groups concept in that method in my normal subgroups method suggestion and ai invented that from my such suggestion (which ai invented the actual method from my suggestion which were same method but different utility of quotient group concept) indeed and i think its a brilliant methodology that ai invented there from my suggestion ) that being one top most method on how to create alternate designs other than rebco, as i last days talked with ai about keeping colimit same but creating more translated versions which would have free groups alike structureness alike suggestion I had with me forgetting about that functor concept from cat. theory and left adjoint-right adjoint functors concepts. and then turned out what i suggested that were exactly that left adjoint right adjoint methodology to ai but not with that definitions but with same translated or functorized definitions indeed. and ai saw directly as of it as a functor and then so i also asked whether if we could defined rings on the functor's more structured side and then ai defined alternate spacecraft hull designs based on those.
so but by until today, I had no knowledge that i were doing suggestions of rebco alternates design (commute graph alternate designs) based on cat. theory since i even forgot what functor were. but so then I studied to cat. theory basics today of brief of introduction to cat. theory book I studied to 2.5 years ago or so. which i definitely forgot all info I had studied to. and ai's brief were very definitive and very fast forwarded me to restudying to that book and also learnt more exactly what some issues I had in that intr. to cat. theory book. hmm so its a blessing to study with ai since ai is like a maths professor you can ask queries to which such chance does not exist when studying from such book.
so these time, i had to study lots of such books again (e.g. without ai, were requiring studying to 500 pages book again and that were very effort requiring as you can infer but with ai i could just restudy in a 4/5 hours or so every single book that needed to be restudied. so it were utter time shortening effort that meanwhile such study were urgnetly required on desining alternate designs extensions to rebco + normal subgroups based methods/free groups and rings translation methods and to extend even hull design methods more, one requires to relearn these basic knowledge of topoi/cat. theory/group theory (Abstract algebra) and then followingly to learn commutative algebras/sheaves-homology/cohomology/algebraic topology concepts which some of such studying i would tackle on tomorrow.
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