hmm enthusiastic days --> imho i would be able to finish necessary study to category theory in following 3 days or so to move to topois topics then and category theory based type theory yayyy then intuitionistic maths and constructivst maths like agda and coq alike checkings. although agda or coq like tools wouldnt be the base tools but rather they might help but basis would be constructed with categorical theory based type theory. 

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