I'm a undergrad(third year, Manchester uni) that is thinking of doing a PhD in this area or category theory in general.
Just wondering, what branches of Maths should I focus on? As I've been told that topology particular Algebraic topology is the main area for this. A lecturer told me I should focus on getting down Algebraic topology before thinking of doing category theory as most of the examples of category theory are from algebraic topology.
However, another lecturer told me I should be doing logic and particular model theory. I can take a course in it this year, but would mean not doing commutative algebra.
But, I'm confused on what I should be studying. Like do I need logic or do I need analysis and algebra?
Also, do you need set theory to do category theory?
P.S. It just seems like every lecturer I asked gives me different answer. Like some even was telling me that I should be doing computer science modules and graph theory.