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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

20 votes
4 answers
2k views

Expressing the Lebesgue integral using categories + the difficulty of describing estimates i...

In this question of mine in a comment to the accepted answer, someone remarked: There are ways to express even basic things in analysis, such as the spectral theorem or the Lebesgue integral, us …
10 votes
4 answers
6k views

'Category-theory'-free areas of pure math, 'category-theory'-loaded areas of applied math

To put it short: In which active research areas of (pure) mathematics no (or only minimal) knowledge in category theory is required ? To put it long: I know almost nothing about category theory - but …