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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeSep 11th 2021

Thought I’d start something in the hope that experts will say more.

• CommentRowNumber2.
• CommentAuthorTim_Porter
• CommentTimeSep 11th 2021

David. Have you seen this?

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeSep 11th 2021

• CommentRowNumber4.
• CommentAuthorvarkor
• CommentTimeOct 9th 2021

Mention KZ doctrines and remove duplicate link.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTime5 days ago
• (edited 5 days ago)

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: