This is an introduction to category theory. We will cover basic topics including categories, functors and adjunctions, as well as limits and colimits. Further topics include Kan extensions, the adjoint functor theorem, and the Barr-Beck monadicity theorem. These notions will continuously be backed up by examples from several branches of mathematics.
There are few formal prerequisites for this lecture. That said, the general categorical notions will be explained with examples from several branches of mathematics such as algebra, topology or functional analysis. It is therefore highly helpful to have basic knowledge of at least one of these fields.