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Dec 4, 2022 at 15:11 comment added Z. M I wonder how "powerful" is this internal language of a 2-topos, or an n-topos (before going to infinity level)?
Dec 4, 2022 at 2:36 comment added Arshak Aivazian According to this comment, my questions 1 and 2 are still too open. I accept the answer.
Dec 4, 2022 at 2:34 vote accept Arshak Aivazian
Dec 3, 2022 at 22:32 comment added Arshak Aivazian Thank you very much for this perspective. Your third paragraph is exactly in the spirit of my question, I really wanted to hear something about it! But what about my questions 1 and 2? Isn't it true that the expressive means of the $\infty\text{-}\rm{Groupoid}$ internal language are much richer than HoTT?
Dec 3, 2022 at 18:24 history answered Tim Campion CC BY-SA 4.0