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• CommentRowNumber1.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 26th 2019

Updated Eric’s webpage.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 26th 2019

Eric’s CNRS Research Proposal is an interesting read. A couple of items I’d like to hear more about:

the terminal example of a polynomial monad turns out to be quite interesting: it is the universe Type of type theory itself, equipped with the operation of dependent sum $\Sigma$. (p. 8)

any dependent family $P:X \to Type$ can be used to generate a left exact modality in type theory. (p. 13)

It seems that first point is along the lines of the section polynomial monad: Relation to object classifiers.

• CommentRowNumber3.
• CommentAuthorAli Caglayan
• CommentTimeFeb 26th 2019
• (edited Feb 27th 2019)

@David the second point is Theorem 3.10 in arXiv:1706.07526.

Edit: No its not.

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 26th 2019

Ah OK, thanks.

• CommentRowNumber5.
• CommentAuthorMike Shulman
• CommentTimeFeb 26th 2019
• CommentRowNumber6.
• CommentAuthorDavid_Corfield
• CommentTimeFeb 27th 2019
• (edited Feb 27th 2019)

I see. So it’s about describing $(\infty, 1)$-toposes via presentations rather than sites (slide 69).

PSp [parameterized spectra] is arguably the main protagonist of ∞-topos theory (slide 20)

is a bold claim.

I see Mathieu in now based in Philosophy at CMU, and has some interesting reflections at his site.

1. has some interesting reflections at his site

I don’t think I’ve seen the following before!

Verdier duality, which is measure theory on topoi.

• CommentRowNumber8.
• CommentAuthorMike Shulman
• CommentTimeFeb 27th 2019

it’s about describing $(\infty, 1)$-toposes via presentations rather than sites

That’s one way of saying it. Another way to say it is that they’ve finally found the correct $\infty$-categorical notion of “site”.

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