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David. Have you seen this?
Mention KZ doctrines and remove duplicate link.
I have edited this entry a fair bit:
Have touched the original text to make it flow better (I hope) and added some crucial cross-links, such as with ETCC and with 2-topos.
Then I added paragraphs on how:
in one direction, this “formal category theory” is the categorification of the discussion of set theory via the topos of sets,
while, in the other direction, it further categorifies to the untrodden territory of formal $\infty$-category theory seen in the full $(\infty,2)$-topos $Cat_{(\infty,1)}$
which however is already interesting in Verity & Riehl’s “formal $\infty$-category theory” seen in “just” $2Ho\big( Cat_{(\infty,1)}\big)$,
(which, at least for the case of presentable $\infty$-categories, is accessible already as 2Ho(ComModCat).)
As one source I found for exactly this terminology, I added pointer to:
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