MTH432 Introduction to Category Theory

These are very broad ideas. You will need to specialise the topic a lot further to get a reasonable topic.

1. Yoneda lemma and applications to posets/groups/rings/topological spaces

2. Adjoint functors and applications to posets/groups/rings/topological spaces

3. Monads on some standard and simple categories.

4. Algebraic Categories, Kliesli categories

5. Elementary Topos and categories associated with open sets of a topological spaces

6. Category theory and computation