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0 pointsspekcular5y ago0 comments

Can you please explain to me how learning category theory is relevant to, or would enhance the work of, a research mathematician who works on, say, harmonic analysis or probability theory?

What is the actual loss to these mathematicians?

Also, your claim that category theory is a foundational theory (in the sense that set theory is) is just mistaken. Homotopy type theory claims to be such a theory, but homotopy type theory should not be identified with category theory more broadly.

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Koshkin5y ago

I wouldn't try, but Helemskii's Lectures And Exercises on Functional Analysis show all this in exquisite detail.

The Convenient Setting of Global Analysis (freely available as a PDF) makes extensive use of the categorical notions and methods.

spekcularOP5y ago

This does not answer my question. The material in the first book is all well-known. A standard reference is Reed and Simon's Methods of Modern Mathematical Physics. Categories don't gain you anything there, and in any case it's tangentially relevant to most work in harmonic analysis and probabiility. The second book is not relevant at all.

Just because you can produce books on analysis where someone uses the word "category," does not mean a working mathematician ought to care.

Koshkin5y ago

(Funny that you mentioned "a working mathematician.")

Anyway, wouldn't it be nice to really understand, on some (higher, admittedly) level, what it is that you are actually doing? Functors and all...

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0 pointsspekcular5y ago0 comments

Can you please explain to me how learning category theory is relevant to, or would enhance the work of, a research mathematician who works on, say, harmonic analysis or probability theory?

What is the actual loss to these mathematicians?

0 comments

Koshkin5y ago

I wouldn't try, but Helemskii's Lectures And Exercises on Functional Analysis show all this in exquisite detail.

The Convenient Setting of Global Analysis (freely available as a PDF) makes extensive use of the categorical notions and methods.

spekcularOP5y ago

Just because you can produce books on analysis where someone uses the word "category," does not mean a working mathematician ought to care.

Koshkin5y ago

(Funny that you mentioned "a working mathematician.")

Anyway, wouldn't it be nice to really understand, on some (higher, admittedly) level, what it is that you are actually doing? Functors and all...

1 more reply

j / k navigate · click thread line to collapse