Ninja Workshop on Category Theory

A `mini-conference' aimed at graduate students (although all are welcome! ) who wish to understand and learn to use (flashy!) techniques from category theory. An appreciation session of abstract nonsense, if you will.
The tentative schedule can be found below. Day one will consist mostly of preliminary material to topics in day two. Day one is aimed at anyone unfamiliar with the material, or those looking for a refresher session. On day two several topics are treated that are hopefully unfamiliar to most, and should provide participants with examples how category theory is applied and can help you in your research.
Talks will be given by participants. If you are interested in attending, please fill out the google form.
If you wish to give a talk, or have suggestions for further material/another talk for day two, please write so in the google form or e-mail me.
The conference will be informal in nature, with a lot of room for discussion.


Day One (8th June) Basic Nonsense JCMB 5327
9:45-10:45 All is One (Zen in Category Theory) Tom Avery Yoneda Lemma/Embedding, Universal properties Scanned Notes
11:00-12:00 Limit Yoga Jenny August Limits, (co)continuity of hom, rewriting limits in set, etc Scanned Notes
12:00-13:30 Lunch Break
13:30-14:30 Yin/Yang of Adjoints Juliet Cooke many (!) examples, interaction with limits, general adjoint functor theorem
14:45-15:45 Monadology Tim Weelinck Monads, their algebras, many examples,monadicity theorem and applications Scanned Notes
16:00-17:00 Exercise Session
Day Two (9th June) Ninja Basics and Applications JCMB 5327
9:45-10:45 Coend Fu Graham Manuell Ends, Coends, Ninja Yoneda Lemma, Density Theorem Slides
11:00-12:00 All Concepts Are Kan Extensions Tom Avery Scanned Notes
12:00-13:30 Lunch Break
13:30 - 14:30 Elementary (ha-ha) Aspects of Topos Theory Matt Booth Presheaves and free cocompletion, grothendieck topologies and topoi Notes
14:45-15:45 Tannakian Techniques Tim Weelinck Reconstruction theory for affine group schemes, algebras and Hopf algebras Scanned Notes
16:00-17:00 Category Theory and Computer Science Thomas Wright Slides


References for day one (and also day two in fact) include, but are not limited to:
  • Categories for the Working Mathematician - Saunders MacLane
  • Basic Category Theory - Tom Leinster
  • Category Theory in Context - Emily Riehl (available on her webpage)
  • Prerequisites

    Very little background on category theory is assumed from the audience, however, we will not start at completely square zero. We assume the reader is familiar with the notions: category, functor, natural transformations, isomorphism and equivalence of categories. Basically either chapter 1 in Riehl or chapter 1 in Leinster or chapter 1 (maybe a bit of 2) in MacLane.