>>12169454>HoTTRead up on algebraic topology and become comfortable with the category theory presented in the book. Hatcher is fine
>Functional Analysismake sure you can do baby rudin up to chapter 6, at least the first 4ish chapters of Folland, and some of papa Rudin. Then Lax or Kadet's book will be good. Honestly, you could also do Reed and Simon's as well
>Lie group theoryLinear algebra, familiarity with abstract algebra, and introductory analysis at the baby Rudin level should suffice to start learning. Procesi's Lie Groups is hard but develops most of the machinery in the book
