The Kan Extension Seminar


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.


This (northern hemisphere) spring, from early January to late June 2014, I will run an online (“extension”) Kan seminar in category theory with the aim of reading the twelve papers listed below. I am seeking between 6 and 12 participants who, in addition to engaging with all of the papers, will compose one or two blog posts for the n-Category Café over the course of the six 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 discussion (likely via Google hangout) on the paper in question, tentatively 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 June 29th in conjunction with the 2014 International Category Theory Conference at Cambridge, UK.

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



As a prerequisite, students should be comfortable with the material found in Mac Lane's Categories for the Working Mathematician or its equivalent. Anyone is welcome to apply but preference will be given to current graduate students (at either the masters or PhD level).

To apply, please email me a single PDF file containing the following:

You may append your CV if you wish. Finally, please indicate whether or not you expect to attend the 2014 International Category Theory conference in Cambridge (June 29-July 5th).

Application deadline: November 30th, 2013.


I am delighted to announce the following participants in the Kan extension seminar. You will be hearing from them shortly 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.  


Please join us at the Winstanley Lecture Theatre in Trinity College from 2pm-6pm on Sunday 29 June for a series of short expository talks. At the conclusion, we will walk together to the welcome reception for the 2014 International Category Theory Conference.

2:00pm-2:30pm  —  tea & conversation


3:50pm-4:10pm  —  tea & conversation



My contact infomation can be found on my personal website.