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import Mathlib open CategoryTheory theorem exists_sequence_of_distinct_adjoints_nat : ∃ G : ℕ → (ℕ ⥤ ℕ), Function.Injective G ∧ (∀ x, (G 0).obj x = x + 1) ∧ (∀ n, Nonempty (G (n + 1) ⊣ G n)) := by sorry
