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tmlxyzab 5 hours ago [-]
Some information about the insights this concept gives us or applications would be helpful.
When Grothendieck and collaborators introduced category theory into algebraic geometry, they had in mind simplification of existing concepts through generalization (produced countless new insights like Grothendieck–Riemann–Roch, Weil conjectures, Hodge Theory, ..). Today, category theorists stack abstraction upon abstraction, and while some of it is certainly useful (higher categories in geometric Langlands for ex), not a lot seems to get simplified anymore. In many cases the category theory seems even more convoluted than what it wants to generalize.