yep -> 

- I finished chapter 4 finally then finished chapter 5 with skipping some of paragraphs in that because I have to read some more basics regarding push outs /epics/monics etc more.

then i due to curisoity started reading chapter 6 and chapter 7 also to come to Tarskian intuitionistic maths and semantics definitions which i had not studied yet.  

imho its now time to revise again some chapter 3 to have some proficiency in chapter 5. ok chapter 4 were understandable (although initially challening) but chapter 5 requires very much proficiency with epics/monics/pullbacks/pushouts much more than chapter 4. 

hmm in between I newly came to understand some basical topo -> logic bijection systems through characterization functions. but not yet read just checked the chapters to study yet. 

hmm,  so now ->

- lets revisit some chapters to take notes and get more proficiency in epic/monic/pullback etc etc

- then revisit chapter 5 then continue learning path for logic system formalisms and later intuitionistics maths on other days since its by itself a lot information to study to these formal logic system formalisms. not study exactly on today. but today lets finalize chapter 5 with some more proficiency in epic/monic/pullback/pushout stuff. 

hmm currently thinking of how to set up there exists and for every quantifiers in these todays learnt topics. e.g. how could we merge A and B with A,B object of category C topos type but to merge their characteristic functions for intersection of A B inclusions somehow to define e.g. for such case, to define for every concept. (e.g. for every x e A to also e B to  have both A and B traits like some set theoretic definition struct ) 

and for there exists, imho, then we would need sampler relation for depicting element of B concept in similar diagram but instead of B  first a set of B to be included in such diagram which is also inclusion map wise connected to B either.  

yep so until i get expert in epic/monic/pullback/pushout topics very much, it might be harder to assemble these diagrams.  imho such diagram i described would be intuitionally much better than yesterday's read adjoint based definition set which did not very well stated and concept there of etc. 

yayyy first task is then to define for every and there exists quantifiers in first order logic systems via such topos constructs but this requires getting some expert in epics/monics/pullbacks which i am not yet. 

but i think even i had not yet become proficient, some knowledge to this topos topics has had been started to be setup. but need to be very proficient.

but already liked the possibilities of capability of this system to enable trait based set definition capabilities of set theoretic approaches. 

hmm also liked the fact that it conceptually really would enable bijective map between concepts to diagrams. e.g. for every concept with set theoretic trait setting etc etc. nor for there exists etc etc.

wov this really is a cool formalization system.  

the missing methodology to define concepts to ml algos.  From there exists to any functorial concept either.  

or the lattice based higher order logic systems etc, could be utilized in various algebras and even groups categories algebras etc etc.  of poset based topos etc etc. 

wov completely amazed by this topos topic I am newly learning of. since its like a best ever programming language alike where you can even code the compiler directly :D 

since been working with Alonzo type programming languages with lambda type functoiralism definitions, and so,  this new formal system seems much better and more semantically fastly interpretable.  plus if you convert computer language to this language based definitions, you can do inferences of the computer code much better, although np complexity wouldnt be reduced either, but again, it can be a methodology to define   semantics of computer programs and direct code structure also  with also thinking of heap based memory system iterations with kripke's semantics alike methods. 

wov this is a nice method to parse computer programs even or to make it defineable in such language of diagrams. 

hmm that be the only part of task of how to make ml algos understand written code and do inferences of its purpose section (since it would need to be able to code, it would learn with also reading exising coding examples) 

wov then it could be able to code the qft calculator /model creator itself via such methodologies.  that formalisms it defines with group theoretic and category theoretic constructs then it would be able to write code to test out simulations and also would might invent group theoretic methods to define new modelings there to how to perturb / parametrize and iterate in its search for quantum computer design ideas. e.g. both quantum computer molecular design ideas and its algebra alternatives. /probabilistic definition alternatives etc etc. 

e.g. in trying to find the outside hadron group (undeciphered yet hadron group) which has relatedness to existing known hadron groups. formulating ideas on that, writing some simulations on assumptions, and creating test setups to test via its own tests (e.g to create multiverse based technologies design task e.g. spacecraft to sail in multiverse etc. ) 

hmm I quite very liked this maths formalism invented by Lawvere. it enables clearly defining concepts to machine. (starting from there exists or for every  etc) (Highest level programming language inventor badge we coders wish to suggest to Lawvere for having inventing best programming language invented ever.:)  )  

this is really some very elegant formal system language design imho.  

I already started to think ideas of how to represent basic verbs.  taking intuition from kripke methods of posets based dynamic system time aspect. but had not read also lawvere paper for alternative dynamic system defintiions either. 

or the ontology definition sets of ontology db. 

after learning topos moment is an aha! moment to project. since it provides an elegant representation method to define part of speech or verbs or other parse tree tags  to machine very clearly. 

I were still going to define them with a maths DSL but none as elegant as topos. 

I mean it really reduced the complexity of  many hundreds many tasks ahead in following 30 days,