Introduction to Category theory
House keeping
This is a WS25/26 course at the Ruhr-Universität Bochum. It can be taken in different
modules of the Bachelor or Master of Science or Art in Mathematics. I am teaching
the second part of the course.
Description
The purpose of this course is to give an introduction to the language of categories
and to illustrate its use in several areas of pure mathematics. We start by introducing
basic notions (Categories, functors and natural transformations,
Yoneda's Lemma, Universal properties and Adjunctions). This first part follows
closely the book
Categories in Context by Emily Riehl.
We then focus on categories of modules over a ring to prove the famous Morita theorem,
as a first big example. Depending on the interests of the audiance we can give
short introductions to more advanced topics such as: categorification,2-dimensional
TQFTs, derived categories...
Prerequisits
Having encountered the notion of morphisms in topology or algebra will be useful.
Lecture notes
My handwritten notes are available on the moodle page for the students. Depending
on my schedule, I sometimes manage to type notes that look nice enough to be put
here.
Exercise Sheets
There is one exercise session every two weeks.
Remarks
The aim we had with Azzurra in teaching this course was to give the opportunity
for student to go through the technical details of results that they tend to
learn on their own and use as black boxes. Some students seem to enjoy this while
others find the details slightly trivial. As a final remark, there were about
four students that attended the class regularly.