hmm studied sheaves then at monoid topos had some pause/laziness. (since learning of sheaves were a challenge it self :D I needed to give pause/break/ some resting time afterwards:D ) (i undersood sheaves the second time i read/studied to not the first time :D) 

also, still not good in learning/fast thinking  of evaluation function concept and exponentiation concept. (of converting the maps to objects in these topos) that section i need to revisit.   (that section in topos side has not been very clearly defined)

ahahaha this studying of topos is quite a challenge. and funny in times-> e.g. first time i read sheaves, I be like -> what the heck this is? what this means?  then some hours later the secondtime i study this time i understood. 

it were like initially --------------> whaaat

since it differs some quite alot from previous topos, i had momentarily confusion moment :D  

same like moment also happent in yoneda lemma  in Tom Leinster's book :DDDD I also had not understood it the first time i read it :DDDDDDDDDDDDD like moment of ------------> whaaaaaaaaaaaaaat? :DDDDDDDDDDD

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nevertheless, I understood this topos type in second reading some hours later :D then came up finally to monoid action topos which i then give some break before reading that:D

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i already started to like topos meanwhile. some topic that challenges me in learning that i have read second time to even be able to understand some sections of :) ( funny talk in the sense, it would had seems like if there is not much msc/phd books that challenges me, whilst situation is the contrary ->  challenging topics set----------> most of msc/phd topics :D  :DDDDD sometimes bsc also challenges but most times bsc topics not very much challenges and instead bores alike. ) 

:DDDDDDDDDDD\

but still, this mind always likes moments where it struggles -> eg. reading some text which it did not understood.  its much better than boredom encountered in learning/revisiting bsc topics chapters whihc is always severely boring. 

same moment happent in robert derekson's one paragraph which i left the book and bought first 2 new books to understand that paragraph there :DDDDDDD ( to learn representation theory first to then be able to understand that paragraph then (in that case, it were hopeless to understand until i learn some representation theory and wraith groups alike (this second book i hadnt studied yet) ) ) hmm i had not continued yet derek robinson's book remnant chapters yet. (but postponed since currently unnecessary for this iteration of ml algos project (group theory advance optimization library would be relevant in post 1.0 versions of ml algos project).  

 the new maths formalization systems based on category theory is really a new paradigm wtr earlier maths formalization systems. i mean category theoretic maths constructs is a complete new world (invented in 1960s alike that I newly learn of)  

 ahaha wuold build medieval times linguists choice NLP design but via modern category theoretic constructs:)

ahahaha still making very much fun of my NLP design of ml algos project layers :D

nevertheless, I want to build a cartesian system unlike the one shot language models systems which discovers language patterns itself with self attention patterns and transformers. that latter is one most successful NLP approach but I dont have resources to follow such contemporary approach but rather switched to very cartesian approach. (like unifying maths and linguistics which is a medieval linguists choice of linguistic studies approaches very funnily :DDDDDD  ) 

--->  ok that be the only layer (NLP side of project)  where medieval linguists technique(of translating NLP construcs to math DSLs)  is applied. other layers are contemporary practices /modern ml approaches.  

 :DDDDDDDD funny project :DDDDDDDDDDDD due to medieval linguists style NLP technique in one layer of project :DDDDDDDDDDDDDDD

but even if i had more time resource to spare to project, I would still go with medieval approach in linguistics, cause underlyingly I like cartesianism.  I dont like Tarskian approaches like the part is larger than whole (making some here maths satire of adjoints of the whole is larger than parts concepts of anti-abstractionist/anti-cartesian philosophies, which I do not apply in design but rather go full cartesian. )  I mean I do not follow common contemporary linguistics approaches since its not expecting to be a very well an NLP project either.  plus I always disliked anti-abstractionist philosophies. and I find the automated dicrete manifolds shaping/iterating systems through data (neural nets) kind of lessened cartesianism level although such systems are much more successful in NLP domain and other fields.  but I would rather follow my medieval linguists choice of linguistic style in my project since its very cartesian (the engineering design approach I like most :)  (cartesianism/positivism, although intersects with funnily medieval linguists style of linguistics science :DDDDDDDDDDDD) 

the visionaries be the new approaches(neural net) of course in these fields. I mean neural net based systems are the visionaries in NLP field (not we medeivals approaches are the visionaries of course. i mean since they advance these fields, i mean new approaches like transformers/self attention etc etc they create new paradigms/inventions in NLP side of course. we the medieval approach followers are not the visionaries of course.).   

but, I go medieval style in this NLP topic of this project (although i use NLP libraries which are following modern approaches for some of NLP tasks) 

hmm for vision of robots (quantum computer/cylotrons alike tech building robots),  I would also of course choose neural net approaches also.  

but for thinking/talking, I would go cartesian since its less anti-abstractionist. (e.g. of course if you go cartesian never forget banach tarski paradox and do not forget to build cartesian system that is possible to include also paradoxes is one other design principal) I mean my cartesianism is not alike hard positivists cartesianism (before 1900s style cartesianism)  of course we would include the banach tarskian paradox definition capability and to include that also in abstract algebras of course. i mean when saying adjoint of the whole is more than parts like philosophies which are anti abstractionist, I do not then think the one possible adjoint of it e.g. of tarskian philosophies are to be excluded in abstractionist philosophies either. actually if you think whole is not the sum,  it does not mean you still can not model it cartesian wise.  of course it would always be only relativistically valid. you would never reachout the actual validity of defined struct in any case, but again, it does not mean cartesianism is unvaluable approach either.  but i just dislike the leaving out abstractionism as unvaluable approach in such philosophies. but of course there neither philosophy is left out and have still alot followers.    

i mean emergentist approaches, ok nice approaches but again, i would follow cartesianism since i dont have time to test/build emergentism :).   (i mean the whole is more than sum of parts approaches alike emergentist/some level anti-abstractionist approaches) 

not that neural nets lacks generalization abstraction skill. on the contrary they have such skill inherently. (e.g. Convolution network usage in NLP neural networks or else multi level encoder-decoders (unlike single layered transformers) )  many have already advanced abstraction skills.

but its encoded inside the discrete manifolds of parameters of neural network.  (although there happens some encoder networks which also encodes the abstraction itself) 

I would rather want my parameters to be category diagrams thats interpretable alsodirectly. (although not easily, since it would be a huge interconnected tree of diagrams of knowledge graph)

but imho that would be possible also for transformers/self attention mechanism including type neural networks either possibly with some mechanisms of discrepancy mechanism. but again, its a style/choice. I also dont have time resource to train neural nets( modern approaches).  cartesian approach is for project required time  wise more economic in this case of me being the only engineer working to build this project.  

but if it were a team, i might followed also new type approaches like neural nets based systems but hmm currently i dont have such time resource for such design choices.

(as mentioned the project needs to be finished in like following 30 days or so)  

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meanwhile->

I would never stop making fun of medieval aspect of this project, that it has in NLP side medieval design principals. That e.g. 2 year ago, I were studying to solve NLP tasks conundrum /design of NLP layers of project. then I though decided to translate constituency/dependency information /parse trees of sentences to entirely math DSL graphs.  and I thought initially this conversion of grammar and semantics to maths is a unique new linguists idea. then later I came upon to learn that, this is the medieval linguistics algorihtm choices :D (that i were aboiut to brag about unique NLP design aspects to only discover some later that its actually medieval linguistics style :DDDDDDDDD)  this funny mooment of project, i think i woulr rereference many times. since it were truly funny. i mean thinking i invent some new design approach to NLP side (how much ignorant in linguistics science i am is visible from that :D)  than turns out its the medieval times linguistics approach :DDDDDDDDDD  not a new paradigm any at all :DDDDDDDDDDD )(ok I would never stop of making fun of this funny moment of project and this funny NLP layer being following medieval times linguistics design principles topic :DDDDDDDDDDDD) 

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