If logic can study the bedrock that the great edifice of mathematics is built on, category theory looks at the already built city and explores architectural themes and similarities running through all kinds of mathematical neighborhoods. Category theory is a discipline a bit like the academic discipline of comparative in that practitioners are expected to be able to cope with comparative literature in not just one, but several languages. It could be argued that category theory is the most difficult place under the whole mathematical umbrella. You need to do something most math PhDs are never taught.
Also, it is perhaps a tribute that my thesis advisor, who was a category theorist, was able to effectively supervise a thesis ...
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