November 18, 2014

The Kan Extension Seminar in the Notices

Posted by Tom Leinster

Emily has a two-page article in the latest issue of the Notices of the American Mathematical Society, describing her experience of setting up and running the Kan extension seminar. In my opinion, the seminar was an exciting innovation for both this blog and education at large. It also resulted in some excellent posts. Go read it!

Posted at November 18, 2014 12:54 PM UTC

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Re: The Kan Extension Seminar in the Notices

Thanks, Tom.

To those who participated, or read a few of the blog posts, what did you think about the seminar? What would you change?

Posted by: Emily Riehl on November 18, 2014 5:22 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

I’ve said this to you before in private, but I’ll say it again in public: I thought it was fantastic in just about every way.

There was only one negative that I noticed, which was that a significant minority of the participants seemed not to ever comment on other participants’ posts. As you wrote:

Most of the students were legitimately hesitant about posting comments early in their careers that will remain publicly viewable in perpetuity.

My perception (not that I was counting) was that a few of the participants commented on just about all the Kan posts, a few chipped in occasionally, and a few said nothing in public outside of their own post. It may be that they were making big contributions to parts of the Kan seminar that I didn’t see, e.g. the private sessions. So I’m not even completely sure that it is a negative.

Of course, you can’t force people to comment online, and a lot of people (students and otherwise) are uncomfortable with commenting on blogs, for understandable reasons. Maybe it’s a matter of clear expectations. A future Kan seminar leader may need to decide whether they expect every participant to take part in the public conversations, and, if so, check carefully with each applicant that they’re comfortable with that.

But maybe it’s OK that only a few of the participants took part in the public conversations. I don’t know.

Posted by: Tom Leinster on November 19, 2014 10:34 AM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

Your guess is correct. Each and every student made a substantial contribution to the non-public parts of the seminar. My most frequent comment on the reading responses was along the lines of “that’s a great observation, which I hope you’ll share on the $n$-Category Café.”

Personally, I wouldn’t feel comfortable mandating online participation, much like I don’t typically insist that all of my on-campus students answer questions in class. Rather I try and do all I can to encourage everyone to speak up, even with partial conjectures that might turn out to be wrong. With some classes I have more success than with others.

Along those lines, what could I do to make students feel more comfortable with commenting online? More broadly, what could we do, as hosts of the $n$-Category Café, to encourage more people (and not just “experts”) to contribute to the discussions in the comments?

Posted by: Emily Riehl on November 20, 2014 5:04 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

More broadly, what could we do, as hosts of the $n$-Category Café, to encourage more people (and not just “experts”) to contribute to the discussions in the comments?

I think to some extent, the comments are likely to mirror the posts. Over the last few years, there’s been a tendency for posts to get both weightier and less frequent. (I’m sure I’ve contributed to that trend myself.) If you look back at the Café five or more years ago, there were more off-the-cuff shorter entries. And with that, maybe potential commenters felt a bit more able to chip in without great expertise.

On the other hand, I think there are always going to be a lot of readers (probably the large majority) who don’t ever comment, because for whatever reason, they don’t want to. And that’s fine, I think.

Part of the reason why I’ve written three non-weighty posts in the last few days is that I wanted to re-establish this as a style of post that we have around here - something that you think of, write and post all on the spur of the moment.

Jordan Ellenberg draws a fantastic analogy between blogging and competitive eating.

Posted by: Tom Leinster on November 20, 2014 5:18 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

This is a neat idea: to try and mix it up with posts that are “half-digested” or “bite-sized.” (Here I find myself compelled to run with Jordan’s disgusting analogy… ;)

Posted by: Emily Riehl on November 21, 2014 2:14 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

One thing the Cafe has in common with most blogs, I think, is that as soon as there are 2 or 3 threads of conversation going, it starts to become difficult to keep track of everything that’s going on, and particularly difficult to catch up with everything if you come to the discussion a little late. I wonder if this could be a barrier to entry in the discussion, in addition to general shyness / perfectionism?

Posted by: Tim Campion on November 20, 2014 9:34 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

Tom wrote:

Over the last few years, there’s been a tendency for posts to get both weightier and less frequent.

Yes. Part of the problem is just that bloggers typically become more intimidatingly erudite, and also more distracted by other duties, with the passage of time. In early issues of This Week’s Finds I explained things like $SU(2)$ and the quaternions, because I still found those exciting. Now I’m talking about $\mathrm{E}_{10}$ and integral octonions. It’s bound to seem more intimidating and dry to most people—though to me, of course, it’s an ever more rollicking roller-coaster ride.

If we hadn’t recruited the “second generation” of n-Café bloggers, like you and Emily, just think how dead the blog would be now! Urs decided posting articles on the n-Café was a waste of time compared to adding information to the nLab and discussing it on the nForum. David Corfield got busy being chair of his department. I decided I should separate out my articles on environmental issues and applied mathematics and post them to Azimuth. I still post vast numbers of short, simple, spur-of-the-moment explanations of math and physics on Google+, but somehow that wouldn’t work well on the n-Café.

So, we really need you youngsters… but it’s getting time to recruit yet another generation of n-Café hosts. And — the hard part — we don’t want the next generation to be too intimidated by the old farts.

(They shouldn’t be. Actually, my main problem with the otherwise wonderful Kan Extension was that many of the blog comments were too sophisticated for me to understand, and I was embarrassed to ask the number of dumb questions I’d need to ask to really keep up.)

Posted by: John Baez on November 21, 2014 1:48 AM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

As a participant, I thought the seminar was a phenomenal experience, introducing me to lots of fantastic category theory and category theorists! A big thanks to all the participants, all who joined in at the Cafe or came to see our talks at the CT conference, and especially to Emily, for making it what it was.

Emily writes in the Notices article about the idea of trying to include more participants who haven’t had the “inside track” benefit of studying at one of the relatively small number of institutions where category theory research occurs. This is a really appealing idea! Some minor tweaks might be needed to support less-well-prepared students. Maybe something like an email listserv for questions that come up between meetings could go a long way, hopefully without being too much of a burden on everyone’s time.

Posted by: Tim Campion on November 20, 2014 9:53 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

A very nice article! Having only read the blog posts, I thought it was awesome, and I don’t think I have any suggestions. But I do have a question for Emily: are you planning to run another iteration yourself?

Posted by: Mike Shulman on November 18, 2014 10:19 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

I’m sure I will run another iteration at some point, but I don’t know how soon — offline teaching intervenes.

But I think it would be really great to see what someone else would do with this format. I think students would appreciate having a course with a different focus lead by someone with different areas of expertise: maybe you? ;)

If anyone is interested in taking the Kan Extension Seminar for a test-drive, I’d be more than happy to help facilitate it in any way that I can.

Posted by: Emily Riehl on November 20, 2014 5:07 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

This is the most recent n-category cafe post I can see in my RSS feed. Does anyone know what’s going on with that?

Posted by: Qiaochu Yuan on December 14, 2014 8:34 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

Posted by: Tom Leinster on December 14, 2014 8:43 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

Jacques replies:

I don’t know what “curl” means here, but maybe you do!

Posted by: Tom Leinster on December 14, 2014 9:18 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

I don’t either, but that worked. Thanks!

Posted by: Qiaochu Yuan on December 15, 2014 5:05 AM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

“see Universal Resource Locator”?

Posted by: Jesse C. McKeown on December 15, 2014 11:25 PM | Permalink | Reply to this

Re: The Kan Extension Seminar in the Notices

oh, no, it was probably /usr/bin/curl ...; and U is “uniform”, not “universal”, silly me…

Posted by: Jesse C. McKeown on December 16, 2014 12:58 AM | Permalink | Reply to this

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