The Kan Extension Seminar II


Daniel Kan's influence at MIT persists through something called the Kan seminar, a graduate reading course in algebraic topology. Over the course of a semester, each student is asked to give a few one-hour lectures summarizing classic papers in the field and to engage with each other paper by writing a reading response. The lectures are preceded by a practice talk of unbounded length that is conducted in private, i.e., in the absence of the lead instructor, before the reading responses are due. This format aims to teach students how to read papers quickly and at various levels of depth, as well as to work on presentation skills. At the semester's conclusion, Kan traditionally hosted a party that took advantage of Boston's high concentration of mathematicians, giving his students an opportunity to meet senior people in the field.

The Kan Extension Seminar, piloted in early 2014, was conceived as an online (“extension”) Kan seminar for peridoctoral category theorists. A dozen category theorists plus one facilitator met biweekly for videochat presentations on classic papers in the field. After each seminar meeting, the presenter wrote a blog post summary that was published on the n-Category Café. Some reflections on the first iteration of the Kan Extension Seminar can be found in the December 2014 issue of the Notices of the AMS.


For the second Kan Extension Seminar, I am delighted to announce that I'll be joined by two co-facilitators:

The seminar will follow the same format as the first version. From mid January to mid May 2017, we plan to read the eight papers listed below. For this, we are seeking 8 participants who, in addition to engaging with all of the papers, will compose a blog post for the n-Category Café over the course of the five months, which will be published every other week. The other participants will be expected to comment. On the week preceding each blog entry, the class will have a private video discussion on the paper in question, initially to take place at 9pm GMT on alternate Mondays, with some time adjustment later in the term to account for daylight savings time. The course will conclude with a series of short public expository lectures given, by those able to attend, on July 16 in conjunction with the 2017 International Category Theory Conference at the University of British Columbia in Vancouver.

Please feel free to contact any of the organizers with any questions regarding the course.



The seminar will meet nine times, the first week for introductions with each of the remaining eight devoted to one of the papers in the order listed above. We will meet according to the following schedule (altered midway through to minimize the pain caused by daylight savings time switches):


As a prerequisite, participants should feel comfortable with the material found in Categories for the Working Mathematician or its equivalent and demonstrate enthusiasm for engaging with more sophisticated categorical topics. Anyone is welcome to apply, but some preference will be given to current graduate students.

To apply, please send a single PDF file to “alexanderpcampbell at gmail dot com” or “fo at seas dot upenn dot edu” containing the following information:

You may append your CV if you wish. Finally, please indicate whether or not you expect to attend the 2017 International Category Theory conference in Vancouver (July 16-22). This question is just for administrative purposes; attendance will have no bearing on the selection process.

Application deadline: November 30th, 2016.


We are delighted to announce the following participants in the Kan extension seminar. You'll be hearing from them shortly on the n-Category Café.



The eight participants of the Kan Extension Seminar gave a series of short expository talks at the 2017 International Category Theory Conference on Monday, July 17 from 15:30-17:25.


My contact infomation can be found on my personal website.