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... Ambidexterity theorem, certain axiomatic structures in high-order category theory are involved. I want to further explore the performance of these category theory axioms in singular geometric situations, and whether there are some implicit assumptions that fail in more complex geometric contexts?

Although my idea may definitely seem naive to you, I think it has some exploratory value. The proof of the Geometric Langlands Conjecture is very complex, and the Ambidexterity theorem is a key ...

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