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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 24th 2011
• (edited Nov 24th 2011)
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 24th 2011

Hm, maybe the references given there so far factor through 2-type theory. Anyway, eventually somebody should say something that fits into this entry! :-)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeAug 21st 2012
• (edited Aug 21st 2012)

Next semester our “group seminar”, starting in a few weeks, has the topic “$(\infty,n)$-categories”. I guess I’ll be sort of running the seminar. Last semester we ended the analogous seminar on $(\infty,1)$-toposes with me giving the survey talk, the notes for which now constitute the $n$Lab entry (infinity,n)-category. Now we plan to dig deeper into the details. So I need to acquaint myself with plenty of those details, to the extent that I haven’t yet (which is just a small extent).

As usual, I have a “personal hook” into the topic: there is a certain question that I would like to eventually understand the answer to, and I’ll probably be looking at the entire seminar through this lens. I had recently posted here a link to a little text that describes this idea, at next (schreiber). In brief, the issue is this:

Complete the step indicated in the very last paragraph of Quantum gauge field theory in Cohesive homotopy type theory (schreiber) .

That is: inside cohesive homotopy type theory postulate a map $\mathbf{c}_{conn} : \mathbf{B}G_{conn} \to \mathbf{B}^n A_{conn}$ together with a suitable representation $\rho$ of $\mathbf{B}^{n-1}A$. At least when interpreted in a model such as Smooth∞Grpd, associated to this data should be an extended topological quantum field theory which to the point assigns the “space of sections” of the $\infty$-bundle $\rho$-associated to the $\mathbf{B}^{n-1}A$-principal bundle modulated by $\mathbf{c}_{conn}$, and this should be internal.

The task is: describe / construct this eTQFT in the internal logic, as far as possible.

The result should involve $n$-directed homotopy type theory in one flavor or other. Moreover, it needs to be with all duals.

I really like the approach to this rough kind of problem that Mike was recently suggesting on the blog here. Maybe that’s the lens through which I want to be looking at the whole question.

Mike, did you make further progress with the ideas sketched there, meanwhile? I’d love to know about whatever you have, to the degree that you can share it.

Another thought that crossed my mind was: for the purpose of $(\infty,n)$-cats with all duals, it might be best to go via blob n-categories. Does anyone what the latest status is of relating that theory to models of $(\infty,n)$-categories is?

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeAug 21st 2012

No, I haven’t gotten any further with that idea.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeAug 14th 2018

Can’t see where they’re from.

• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeAug 14th 2018

Can’t see where they’re from.

What?

• CommentRowNumber7.
• CommentAuthorMike Shulman
• CommentTimeAug 14th 2018

• CommentRowNumber8.
• CommentAuthorDavidRoberts
• CommentTimeAug 14th 2018

@David C

You wean where Paige is from?

• CommentRowNumber9.
• CommentAuthorDavid_Corfield
• CommentTimeAug 14th 2018

@David R, yes. I couldn’t find anything to form a page on Paige, but then I am limited to Baidu as a search engine since in China.

• CommentRowNumber10.
• CommentAuthorDavidRoberts
• CommentTimeAug 14th 2018

@David C

note that her surname used to be just ’North’. Here is her current home page: https://paigenorth.github.io/

• CommentRowNumber11.
• CommentAuthorMike Shulman
• CommentTimeAug 14th 2018

Oh, was “they” in #5 supposed to be a singular genderless pronoun? (-:O

Coincidentally, Paige is here with me in San Diego this week, with Benedikt Ahrens and Dimitris Tsementzis, working on a different project.

• CommentRowNumber12.
• CommentAuthorDavid_Corfield
• CommentTimeAug 15th 2018

Seems like a good solution to me. Do you always write “he or she”?

• CommentRowNumber13.
• CommentAuthorMike Shulman
• CommentTimeAug 15th 2018

I do sometimes use “they” as a singular genderless pronoun, but it usually sounds slightly awkward to me because its primary meaning in my idiolect is still a plural. It also didn’t occur to me that Paige’s gender might not be obvious from her name, so I didn’t think of the possibility that “they” in #5 might be referring to her, and was therefore unable to make sense of the sentence. In this situation, if I were unsure of her gender, I would probably just have re-used her name: “Can’t see where Paige is from”.

• CommentRowNumber14.
• CommentAuthorDavid_Corfield
• CommentTimeAug 15th 2018

It’s not a name I’ve ever encountered. I dare say with Google I could have worked out the gender, but try Baidu. Had I known Wikipedia is available here, it wouldn’t have helped so much:

Paige is a given name for males and females. It is of Latin origin (Byzantine “Págius” young boy helper/mate of young nobles, from “padius” young boy, derived from Greek “Paidion” child) and its meaning is “young helper” or “young child”. A page in medieval households was usually a young boy whose service was the first step in his training as a knight. Use may possibly indicate an ancestor who was a page.

In modern times Paige has become a given name, generally given to girls living in North America since the middle of the 20th century, but also occasionally to boys.

• CommentRowNumber15.
• CommentAuthorMike Shulman
• CommentTimeAug 15th 2018

I’m not saying her gender should have been clear from her name, just that at the time, it failed to occur to me that it wouldn’t be. (-:

• CommentRowNumber16.
• CommentAuthorDavid_Corfield
• CommentTimeAug 15th 2018

I’ve been wondering how well the type theoretic usage of contexts captures our interpretative practices. We each have our own context, and then when we speak with someone else, we can theorise as to theirs. This includes what we take to be common knowledge, but we will also envisage that they will have parts different from ours, through ignorance, mistakes, greater knowledge, different experience, etc. Adjustments to our own context and to our model of the other’s context must continually be made as we converse.

On reading ’Paige’, I adjust my context to add, ’Paige: Name of person’. You already have ’Paige: Name of female person’, and a supply of people so named, and take it to be within common knowledge.

It seems we do a lot of work in reconstructing sensibly the contexts in which statements make sense. We often use the language of inference, but it’s better to distinguish presupposition from inference. We hear something, postulate a reasonable context in which it makes sense, then infer some component of that postulated context, and take it to be inference from the original statement. On hearing that X has stopped smoking without knowing anything of his habits, I see that it is presupposed that X once was in the habit of smoking. It’s better to distinguish this inference to presupposition from a proper inference, such as to the claim that X now has a lower chance of a heart attack.