Take the 2-minute tour ×  I'm a undergrad(third year, Manchester
uni and want to do a PhD) that is thinking of doing a PhD in
this area or category theory in general.(Sorry for asking it
here, Maths exchange stack didn't help as asked twice last week
and then today, I spend like an hour a day worrying about what
I'm studying and what I should study). Imagine a chess board and
you need to move a piece, how you know you are moving the best
piece?, now times that by a thousand.  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.  So
before you delete this can you please t