The n-Category Café

Announcing the Kan Extension Seminar

Posted by Emily Riehl

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 plan to 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 will compose one or two blog posts to appear here on the $n$-Category Café over the course of the six months, which will be published every other week. Everyone will be expected to write comments, engaging with all of the papers.

• Lawvere, An elementary theory of the category of sets

• Street, The formal theory of monads

• Freyd-Kelly, Categories of continuous functors, I

• Lawvere, Metric spaces, generalized logic and closed categories

• Kelly-Street, Review of the elements of 2-categories

• Street-Walters, Yoneda structures on 2-categories

• Johnstone, On a topological topos

• Kelly, Elementary observations on 2-categorical limits

• Blackwell-Kelly-Power, Two-dimensional monad theory

• Adámek-Borceux-Lack-Rosický, A classification of accessible categories

• Lack, Codescent objects and coherence

• Shulman, Enriched indexed categories

On the week preceding each blog entry, the class will have a private discussion (likely via Google hangout) on the paper in question. 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.

More details, including information about how to apply, can be found on the seminar website. Applications are due November 30th. I hope you’ll help me spread the word by passing this message along to those who might be interested.