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.

**SEMINAR**** STRUCTURE**

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.

**READING**** LIST**

- F.W. Lawvere, An elementary theory of the category of sets, 1964, Repr. Theory Appl. Categ. 11 (2005) 1-35.
- R. Street, The formal theory of monads, J. Pure Appl. Algebra 2(2) (1972) 149-168.
- P.J. Freyd, G.M. Kelly, Categories of continuous functors, I, J. Pure Appl. Algebra 2(3) (1972) 169-191.
- F.W. Lawvere, Metric spaces, generalized logic and closed categories, 1973, Repr. Theory Appl. Categ. 1 (2002) 1-37.
- G.M. Kelly and R. Street, Review of the elements of 2-categories, Lecture Notes in Math. 420 (1974) 75-103.
- R. Street, R. Walters, Yoneda structures on 2-categories, J. Algebra 50(2) (1978) 350-379.
- P.T. Johnstone, On a topological topos, Proc. London Math. Soc. 3(38) (1979) 237–271.
- G.M. Kelly, Elementary observations on 2-categorical limits, Bull. Austral. Math. Soc. 39 (1989) 301-317.
- R. Blackwell, G.M. Kelly, A.J. Power, Two-dimensional monad theory, J. Pure Appl. Algebra 59 (1989) 1-41.
- J. Adámek, F. Borceux, S. Lack, J. Rosický, A classification of accessible categories, J. Pure Appl. Algebra 175 (2002) 7-30.
- S. Lack, Codescent objects and coherence, J. Pure Appl. Algebra 175 (2002) 223-241.
- M. Shulman, Enriched indexed categories, Theory Appl. Categ. 28(21) (2013) 616-695.

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:

- Your contact information and educational history.
- The name of a reference as well as his or her contact information.
- A brief paragraph explaining your interest in this course.
- A paragraph or two describing one of your favorite topics in category theory.
- A list of the four papers (selected from the list above) that you would most like to present together with an explanation of your preferences.

Application deadline: **November 30th, 2013.**

** PARTICIPANTS**

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.

- Tom Avery, Edinburgh, Scotland — Metric Spaces, Generalized Logic, and Closed Categories
- Eduard Balzin, Nice, France — Formal Theory of Monads (Following Street)
- Alexander Campbell, Sydney, Australia — An Exegesis of Yoneda Structures
- Tim Campion, Westwood, MA, USA
- Alexander Corner, Sheffield, England
- Joe Hannon, Boston, MA, USA
- Fosco Loregian, Padua, Italy — Categories of Continuous Functors
- Sean Moss, Cambridge, England — On a Topological Topos
- Clive Newstead, Pittsburg, PA, USA — An Elementary Theory of the Category of Sets
- Sam van Gool, Paris, France
- Christina Vasilakopoulou, Cambridge, England — Elementary Observations on 2-Categorical Limits
- Dimitri Zaganidis, Lausanne, Switzerland — Review of the Elements of 2-Categories

** CONTACT**** INFO**

My contact infomation can be found on my personal website.