In the process of proving the 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 conclusion within it. Any potential applicability issues could affect the validity of the proof.
Therefore, I hope to start with the local geometric structure at singular points, further verify the limitations of the theorem and potential problem areas. If you have a better idea, please let me know, your dearest student/grandson, for the first time this week, has felt the trouble of real hair loss."
