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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 26th 2019

    Updated Eric’s webpage.

    diff, v4, current

    • 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 Σ\Sigma. (p. 8)

    any dependent family P:XTypeP: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 (,1)(\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 (,1)(\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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