This is an on demand course. If there are enough PhD students interested, then I will run the course. At the moment the course is running.

Lecture plan

1. Introduction. Definition of partial orders and monoids. Definition of a category and some examples including the Category of sets and functions, the category monoids and monoid maps, a partial order as a category, a monoid as a one object category. Definition of functors and the category of category and some worries about foundations.

2. Some constructions on categories: the opposite category and slice categories. Some properties of maps in categories: Isomorphism, Epimorphism, Monomorphims. Products in categories.

Some Additional Resources.

• A good collection of Links on category theory.

• Tom Leinster’s excellent book is available free online.

• Some notes that might be useful. If you don’t read the notes, then a look at the references, which has pointers to a lot of good resources.

• Emily Riehl’s Book Category Theory in Context contains lots of examples of common constructions in category theory. Some of the examples might require some background in algebra. You can also buy the book quite cheaply from Dover

Old Version of the course

PhD reading course going through Bartosz Milewski’s book on Category theory. Mostly organised by Nikolaus Huber.

Information can be found on:

• Information