Where to study category theory?

Question

I am attending a master in math, and I am very passionate about category theory. Especially, I like how limits extend a lot of results from a little "core" of the category to everything. I furthermore like beatiful algebra, like Galois theory, commutative algebra, homological algebra, finite representation theory...

Unfortunately, in my university there is few of this stuff. Where would you suggest me to go for a one-year exchange program, especially to deepen my categorical (but not logic) interests?

Thank you!

EDIT: Europe would be the best for geographical reasons, but I am open to international experiences. However, it is increasingly harder for me to get an exchange program with far countries (I come from Italy).

Answer 1

You can get a fair amount of category theory in the masters of parisian universities, mainly oriented towards algebraic geometry and algebraic topology. Also, you get a fair amount of categorical seminar around Paris (go figure...).

It depends on the year you attend, but Université Paris 6 (Pierre et Marie Curie) usually have courses on étale cohomology and sheaf theory for algebraic groups. Université Paris 7 (Diderot) usually have courses about homology/homotopy with a categorical point of view. Université Paris 13 (Saint-Denis) offers courses about homotopy and operad theory. Also, most courses can be followed independently of the university you registered in.

A little closer to Italy, there is quite a categorical team in Nice (Université Sophia-Antipolis), mostly around Carlos Simpson and Clemens Berger I would say. Definitely a good place for a categorical PhD, however I'm no sure it reflects into the master there.

Just my two french cents !

Answer 2

At the risk of falling into shameless publicity, my university (Université catholique de Louvain, in Belgium), has a research team in category theory and offers two category theory courses :

• the first one introduces the main concepts (categories, functors, natural transformations, Yoneda lemma, limits, adjunctions), and then covers regular and exact categories before turning to the abelian ones and all the homological lemmas.
• the second one is geared towards the Master students interested in research and the PhD students. Depending on the year, it can cover monads and Lawvere theories, homological and semi-abelian categories, categorical Galois theory...

In addition, there are several courses in algebra and algebraic topology where some amount of category theory is used.